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• Average and Range Spiders - alutwyche on TES
• Average and range fill in the blanks ( answers ) - Dr Austin Maths
• Girls are Better at Maths?  - mathspad.co.uk
• Averages Puzzle  - mathspad.co.uk
• Small data set average problems - Median Don Steward
• Mean lesson - Boss Maths
• Mean matching cards - NCETM
• Mean questions  - @taylorda01
• Median lesson - Boss Maths
• Median and Quartiles Fill In The Blanks ( Answers ) - Dr Austin Maths
• Median questions  ( answers ) - @taylorda01
• Interquartile range - Miss Konstantine
• Wipe out  - Median Don Steward
• Two poems  - Median Don Steward
• Averages and the range worksheets   - Maths4Everyone on TES
• Range lesson - Boss Maths
• Range from a list of data - Craig Barton via variationtheory.com
• Median from a list of data  - Craig Barton via variationtheory.com
• Mean from a list of data - numbers  - Craig Barton via variationtheory.com
• Mean from a list of data - algebra  - Craig Barton via variationtheory.com
• Mean from a list of data - missing numbers  - Craig Barton via variationtheory.com
• Exam questions on averages and the range - Maths4Everyone on TES
• Mean, Median, Mode and Range  - Maths Assessment Project 
• Averages and Range Maths Challenge Questions ( answers ) - Dr Austin Maths
• Averages and range: increase, decrease, same?  - Craig Barton via variationtheory.com
• Venn rich tasks  - mathsvenns.com
• Averages with fractions - Nathan Day
• Averages with surds - Nathan Day
• Frequency tables - MathsHKO
• Messy Means - Maths Sandpit
• Estimating the mean from a grouped frequency table - Richard Tock
• Mean from a table crack the code ( answers ) - Dr Austin Maths
• Estimate the mean from a grouped frequency table  - @fortyninecubed via variationtheory.com
• Estimate the mean from a frequency table 2  - @fortyninecubed via variationtheory.com
• Mode and modal class lesson  - Boss Maths
• Mean of a frequency distribution  - Median Don Steward
• Mean from a frequency table  - @mathsmrgordon via variationtheory.com
• Mode from a frequency table  - @mathsmrgordon via variationtheory.com
• Mean, Median, Mode - mathshelper.co.uk
• GCSE questions on frequency tables - Maths4Everyone on TES
• MathsPad has great resources for frequency tables and averages - subscription required.

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• Bar charts lesson  - Boss Maths
• Drawing Comparative Bar Charts Practice Grid ( Answers ) - Dr Austin Maths
• Drawing Composite Bar Charts Practice Grid ( Answers ) - Dr Austin Maths
• Relating charts to data sets  - Don Steward 
• Data Collection and Presentation chapter - CIMT
• Drawing bar charts - TeachIt Maths
• Trevor's Holiday Project - TeachIt Maths
• Whispers game - TeachIt Maths
• Bar chart and pie chart codebreakers  - alutwyche on TES
• Bar chart problem solving  - groov_e_chik on TES 
• Bad Bar Charts  |  Solutions  - winatschool.org.uk
• Pie charts lesson - Boss Maths
• Drawing Pie Charts Practice Grid ( Answers ) - Dr Austin Maths
• Pie Charts Fill in the Blanks ( Answers ) - Dr Austin Maths
• Primary data question including pie charts  - gerryhall.org.uk
• Calculating pie chart angles  - @fortyninecubed via variationtheory.com
• Pie Charts - Median Don Steward
• Various pie chart resources - Teachit Maths
• Pie chart puzzles - National Stem Centre
• Pie Chart Tasks - MathsHKO
• Blog post about teaching histograms  - Paul Rowlandson
• Histograms lesson - Boss Maths
• Histograms lesson and worksheets - DrFrostMaths.com
• Histogram lesson materials - Don Steward
• Histograms worksheet - m4ths.com
• GCSE questions on histograms  - mathsteaching.wordpress.com
• Interwoven Histograms and Cumulative Frequency - Nathan Day
• GCSE 9 - 1 exam questions - Maths4Everyone on TES 
• Interpreting Frequency Graphs  (textbook extract - includes histograms) - OUP

• Simple stem and leaf worksheet   - nottcl on TES
• Stem and leaf lesson and resources - goteachmaths
• Stem and leaf diagram problems - Don Steward
• More ideas and resources in my  blog post on stem and leaf plots
• Pictograms lesson  - Boss Maths
• Pictograms task  - @giftedHKO
• Interquartile range and box plots lesson  - Boss Maths
• Box plots: increase, decrease, same?  - Craig Barton via variationtheory.com
• Box plots: draw and interpret - alisongilroy on TES
• Temperatures (box plots) - Mathematics Assessment Project
• Cumulative frequency graphs lesson - Boss Maths
• Plotting Cumulative Frequency Graphs ( Answers ) - Dr Austin Maths
• Reading Cumulative Frequency Graphs ( Answers ) - Dr Austin Maths
• Cumulative frequency questions  - Median Don Steward
• Cumulative frequency textbook chapter - Pearson
• Olympic Weights  - NCETM
• Interwoven Histograms and Cumulative Frequency  - Nathan Day
• Cumulative Frequency GCSE questions - Maths4Everyone on TES
• Comparing data sets lesson - Boss Maths
• More ideas and resources in my  blog post on box plots
• Ideas and resources in my blog post on scatter graphs
• Scatter graphs, correlation and causation - Boss Maths
• Scatter Graphs True or False - MathsPad
• Scatter graph resources - goteachmaths
• Simple scatter graph worksheet  - t0md3an on TES
• Scatter graph scaffolded worksheet - misslatham on TES
• ' Bee aware ' activity - Median Don Steward
• Scatter graph questions - Median Don Steward
• Scatter graph hat-trick  - Teachit Maths
• Scatter graphs - TeachitMaths
• Statistical diagrams chapter  (including scatter graphs) - CIMT (see website for answers)
• Scatter graph investigation  - Teachit Maths
• Scatter graphs activities - Phil Hatchard on TES
• Correlation vs Causation Worksheet  - mathworksheetsland.com
• Correlation vs Causation Activities  - sweeney67.weebly.com
• Causation Examples  - lsrhs.net
• Correlation and cause slides  - ceviche on TES
• GCSE 9-1 Exam Practice Questions (Scatter Graphs) - Maths4Everyone on TES
• Tables, conversion graphs, line graphs and time series  - Boss Maths
• Times Series & Moving Averages  - Ryan Smailes on TES
• Time Series Graphs  - mcs123 on TES
• Data Analysis and Interpretation  - CIMT
• Moving Averages  - @ dooranran on TES
• Time Series textbook chapter
• Sampling lesson - Boss Maths
• Paddy Paws, Nisbett and the parrot (data collection sheet design) - Teachit Maths
• My classmates  - Teachit Maths
• Probably the worst survey in the world  
• Interactive biased question sort  - mathspad.co.uk
• Common mistakes survey  - The Chalk Face  (&  accompanying PowerPoint )
• Prezi slideshow 'Sampling'  - to generate discussion about sampling methods (by me!)  
• Types of data - The Chalk Face
• Data types and sampling methods - Teachit Maths
• Data collection and sampling revision cards - Teachit Maths
• Stratified sampling GCSE questions
• Parking Permits (stratified sampling) - student sheet , notes , slides  - Nuffield Foundation
• Capture-Recapture handout and slides - MathsPad
• Capture and Recapture - nrich
• Capture Recapture textbook exercise  - CorbettMaths
• A Lesson: The Capture-Recapture method - MathsMuggle
• Capture-Recapture lesson and res ources - NCTM
• Capture Recapture New GCSE - dannytheref on TES
• 'Something Fishy' project - PBS
• Capture-Recapture Slides - pbrucemaths on TES
• Capture recapture worksheet - youngscientistsmhs.weebly.com
• Select 'Estimating Populations' on the mathsbot.com GCSE question generator
• James Gurung's video explains how to answer an exam style capture-recapture question 
• Mark and recapture garden snails (graphic for practical activity) - The Wildlife Trusts on TES
• See Edexcel Emporium (GCSE 1MA1 Practice papers > Themed papers) for exam questions
• Systematic listing strategies and the product rule for counting lesson - Boss Maths
• Listing outcomes  - Maths4Everyone on TES
• Product rule for counting exercise - Corbett Maths
• Systematic listing and counting strategies - one freee, five with MathsPad subscription
• Three pens - Just Maths
• Product Rule for Counting - Corbett Maths
• Product Rule for Counting - First Class Maths
• Counting Strategies Full Coverage GCSE Questions  - compiled by Dr Frost
• Blog post: Multiplicative counting - the different types from @MrMattock
• Blog post & resource list: Systematic Listing Strategies from @ColleenYoung
• CIMT Probability - KS3 and GCSE - CIMT via TES
• Simple probability worksheets - dh2119 on TES
• Mutually exclusive probability - Richard Tock on TES
• Probability (slides and worksheets) - Dan Walker on TES
• Simple probability match-up - mathspad.co.uk
• Probability resources - Dr Austin Maths
• Theoretical probability lesson - Boss Maths
• Probability and counters - Don Steward
• Probability - Filling Spinners - steele1989 on TES
• Probability Puzzles - alutwyche on TES
• Experimental vs Theoretical probability activity
• Old KS2 probability questions
• Probability KS3 questions - Median Don Steward
• Greater odds - Median Don Steward
• Probability and words - Median Don Steward
• Simple probability - Maths4Everyone on TES
• Probability single event - Maths4Everyone on TES
• Probability mix - Don Steward
• Evaluating Statements about Probability - Maths Assessment Project (activities at the back)
• Introduction to probability  - lessons plans and activities - Project Maths
• Introduction to relative frequency - lessons plans and activities - Project Maths
• Relative frequency lesson - Boss Maths
• Fair or not? - Median Don Steward
• Probabilities from tables - steele1989 on TES
• Sample space scenarios - Teachit Maths
• Sample space puzzles - Teachit Maths
• Determine Probabilities booklet - mathscentre.co.nz
• Could it be a probability?  - Craig Barton via variationtheory.com
• Conditional probability lesson  - Boss Maths
• Probability Full Coverage GCSE Questions  - compiled by Dr Frost
• Exam style questions  - Transum
• Blog post about teaching probability trees - Paul Rowlandson
• Tree diagrams lesson - Boss Maths
• Simple probability trees worksheet (& solutions ) - adapted from original by Georgina Burgess
• Probability trees for dependent events  
• Tree diagrams - Median Don Steward
• Probability tree resources  - Dr Austin Maths
• Tree diagrams - challenge and extension problems - tonycarter45 on TES
• Probability trees - mathshelper.co.uk
• Probability trees workbook - Maths4Everyone on TES
• Probability trees GCSE question practice - Maths4Everyone on TES
• Exam style questions - Transum
• Frequency trees lesson - Boss Maths
• Reasoning with Frequency Trees - Mr Draper Maths
• Frequency trees and percentages - Don Steward
• Frequency trees  - alisongilroy on TES
• Frequency trees - explanation and exploration - DaveGale on TES
• Frequency trees 1 / Frequency trees 2 / Frequency trees 3 - m4ths.com
• Frequency Trees - solvemymaths.com
• Prize Giving  - nrich
• LEARN homework - JustMaths
• Sets GCSE Summary Book - Maths4Everyone on TES
• Venn diagram dominoes - Teachit Maths
• Venn diagrams activities - nottcl on TES
• Structured Venn Diagram Questions  -SiouxzieD on TES
• Drawing and reading Venns - BeenAway on TES
• Sets & Venns Chapter
• Probability & Venn Diagrams Chapter
• Logic and Venn Diagrams  (& activities  & slides ) - CIMT
• Venn Paint - Transum
• Set notation worksheet
• Venn resources  - Dr Austin Maths
• Set notation activity ,  answers , poster  - FMSP  
• Venn Diagram Activities Probability - nottcl on TES
• Venn Diagrams and the Addition Rule - Illustrative Mathematics
• Venn Diagram exam questions  - from Irish exam papers via  @e_hayes12  
• Probability venn diagrams - mathshelper.co.uk
• Independence, Dependence, Mutually Exclusive or Not?  - Payphone on TES
• KS3-4 Bridging the gap Pocket 5 - Set notation, number lines and Venn diagrams  - AQA
• Venn Diagram AQA GCSE questions - collated by the calculatorguide.com
• GCSE (9-1) Venn diagrams exam questions  - aliali on TES 
• Exam Question Practice (Venn Diagrams)  - Maths4Everyone

• Data activities - CIMT
• Representing data check-in - OCR
• Two way tables and frequency tables lesson - Boss Maths
• Two way tables with ratio and fractions  - @mathsmrgordon via variationtheory.com
• US Presidents longevity  task - Median Don Steward
• Data analysis report - HE applications  - Nuffield Foudation
• Data Displayer  online tool - www.actuarialfoundation.org
• GCSE Graphs Revision Summary
• Handling data revision  and Probability revision - rogradymaths.blogspot.co.uk
• Charts and Graphs workout  - Teachit Maths
• GCSE Statistics 50 Quick Questions  - The Maths Magpie on TES
• GCSE Statistics Questions  - via mathsteachers.wordpress.com

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Types of Data Revision

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Filter by exam board, types of data.

We can classify data in a few different ways. First of all, we can classify data into different types by looking at what form it takes, and then classify these types depending on how it has been collected.

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Class 1: Qualitative

Qualitative/categorical data is anything that isn’t a number, for example words. We usually obtain qualitative/categorical data by conducting a survey. Examples include:

• Football team names
• Favourite takeaways

Class 2: Quantitative

Quantitative data is numerical. There are two types of quantitative data, continuous and discrete.

Continuous data can take any numerical value. Examples of continuous data include:

• Running race times

Discrete data can only take certain exact numerical values (typically whole numbers). Examples of discrete data include:

• Number of children

Primary Data

Primary data is data that you collect first-hand.

• Surveying members of the public
• Measuring the heights of your classmates

Advantages :

• You can ensure that the data is relevant
• You can ensure your data sample is reliable

Disadvantages:

• Collecting data can be very time-consuming
• Paying for resources (e.g. printing questionnaires), and/or participation in the survey means that it can be expensive

Secondary Data

Secondary data is data that has already been collected by someone else.

• The results of a questionnaire that have been posted on the internet
• Statistics published in a newspaper
• It takes much less time than collecting data yourself
• Secondary data is either free, or at least much cheaper than collecting the data yourself

Disadvantages :

• The data available might not be suitable for your purposes
• You don’t know how the data was collected, meaning you can’t be sure that it is representative or fair

Note: It’s important to understand that we can combine the two classifications we’ve seen. In other words, data can be continuous and primary / secondary, or categorical and primary / secondary etc.

Example 1: Types of Data

Janet wants to learn some information about Jason. She learns three pieces of new information about him. For each one, state whether the data is discrete, continuous, or categorical.

a) His hair colour.

His hair colour might be brown, blonde, ginger, but in any case, it’s not a number. Therefore, this is categorical data .

b) How many siblings he has.

The number of siblings Jason has can only be a whole number. Therefore, this is discrete data .

c) How fast he can solve a Rubik’s cube.

How fast he can solve the puzzle is given as a time so the result could be any value. Therefore, it is continuous data .

Note: Time is continuous, even through your stop watch may only count to the nearest hundredth of a second for example.

Example 2: Types of Data

Chidi wants to gather some data on people’s favourite food. He decides to use a survey he found online that was conducted 10 years earlier where 200 people were asked if their favourite food was Italian, Chinese, Indian, or, Thai.

a) State which two of the following words describes the data Chidi is using:

                       primary,         secondary,          categorical,         discrete,         continuous.

The data is regarding people’s favourite type of food.  Since this is not numerical, it must therefore be categorical . Secondly, he is using data that was collected by someone else so this is secondary data.

b) State one advantage and one disadvantage of Chidi choosing to use this type of data.

• One advantage of Chidi using this data is that he saves a lot of time compared to collecting it himself
• One disadvantage is that Chidi doesn’t know how the data was collected, so it might not be representative

Additionally, in this case the data is 10 years old and people’s preferences might have changed a lot in that time. Furthermore, the survey he found only gave people 4 choices – it is missing many other options.

Types of Data Example Questions

Question 1: State whether the data for the following is categorical, discrete or continuous:

a)   The heights of 12 dogs.

b)   The lengths of 15 snakes.

c)   The eye colours of students in a class.

d)   The number of goals scored by members of the school’s football team.

a)  Since the heights of dogs can be of any value (including numbers that are not whole numbers), this data is continuous .

b)   Since the lengths of snakes can be of any value (including numbers that are not whole numbers), this data is continuous .

c)  Since the data collected will be in the form of words (blue, green, brown etc.), this data is categorical .

d)  Since goals can only be counted in whole numbers, this data is discrete .

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Question 2: Eleanor is measuring the length of everyone in her class’s hair. State:

a)    Whether this data is primary or secondary.

b)    Whether this data is categorical, discrete, or continuous.

a) Since Eleanor is measuring the data herself, the data is primary .

b) She is measuring hair length, which can have any value, including values that are not whole numbers, so the data is continuous .

Question 3: Tahani says:

“People’s shoe sizes are based on the length of their feet, and since length is continuous, shoe size must also be continuous.” Explain why Tahani is wrong.

Tahani is wrong because although a shoe size is based on foot length, the length of a person’s foot can be of any value, whereas shoe sizes have limited values ( 5 , 5 and a half, 6 , 6 and a half etc.).

Question 4: Michael wants to collect information from families in his town about the number of children they have. He chooses to question people directly to obtain this data.

a)   State whether his data will be primary or secondary.

b)   Give two advantages of choosing to use this type of data.

a)  Since Michael is collecting the data himself, it is primary data.

b) By collecting the data himself, he can ensure that the numbers are all accurately recorded.

A second advantage is that he can make efforts to make sure his sample is representative (he can ask people of different genders, races, ages, etc.).  If he was using secondary data, he would have no control over who was being asked.

Note: other correct advantages are acceptable.

Question 5 :  Steve wants to obtain data from his 30 classmates about the performance of the striker, Harry Kane, in a recent match. Half of them are allowed to choose from the following six options:

• “The worst performance I have ever witnessed from any player ever!”
• “He had a nightmare!”
• “A below average performance.”
• “Not his fault the team lost.”
• “I wish he could play like that every week!”
• “No player in the world could have performed better than that!”

The other half of the class are asked to give him a rating out of 10 .

a)   Is the data that Steve obtains from the first set of data categorical, discrete quantitative or continuous quantitative data?

b)   Is the data that Steve obtains from the second set of data qualitative, discrete quantitative or continuous quantitative data?

c)   State two disadvantages for collecting data qualitatively in this example.

a)  Since the data that Steve collects from the first half of the class is worded data, this is categorical data .

b)  Since the data that Steve collects from the second of the class is a number, this is quantitative data.  Since the data can only take certain values (numbers between 1 and 10 ), the data is discrete quantative data .

c)  The first disadvantage of collecting data in this way is that it is harder to analyse.  It is much easier to analyse numerical data than worded data.

The second disadvantage is that there are only 6 options for the worded responses, whereas there are ten options for numbered responses between 0 and 10 .

Types of Data Worksheet and Example Questions

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Home > Statistics > Good teaching > Data collection > Types of data > Categorical and numerical data

The activity U npacking Categorical and Numerical Data  explores the essential understandings for the two types of data. It does this with an outline for an investigation based on the two questions below: one categorical and one numerical.

• How do you usually get to school?
• How long does it usually take?

You can download the  U npacking Categorical and Numerical Data: Student Worksheet and some sample responses using a random data set in  U npacking Categorical and Numerical Data: Teacher Notes .

This is a highly recommended activity that can be introduced in conjunction with Problems with Categorical Data and teaching advice on medians and categorical data . 

Curriculum links

Year 5: Pose questions and collect categorical or numerical data by observation or survey

Year 6: Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables

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Videos, worksheets, 5-a-day and much more, continuous/discrete data textbook exercise, click here for questions.

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Types of Data

In this data chart instructional activity, students read the directions and study the examples to learn the difference between qualitative, quantitative, discrete and continuous data. Students answer 24 questions. This page is intended to be an online activity, but can be completed on paper.

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Spreadsheets

Spreadsheets are used to store information and data. Once we have our information in a spreadsheet we can run powerful calculations, make graphs and charts and analyse patterns.

How spreadsheets work

The most popular spreadsheet program is Microsoft Office Excel. Free alternatives include OpenOffice Calc and Google Docs, which runs in a web browser .

Workbooks and worksheets

A spreadsheet file is made up of one workbook and multiple worksheets. Worksheets appear as tabs at the bottom of a workbook. They can be reordered and renamed.

Columns, rows and cells

Every cell in a spreadsheet or worksheet has a unique cell reference, which consists of a letter and a number. The letter refers to the column and the number refers to the row.

To select a cell, left click on it. To enter data , double-click it. To select multiple cells, click and hold the left mouse button and drag it in the direction of the cells you want to select.

Entering data into a cell

Data can be typed directly into a cell or into the formula bar. To the left of the formula bar you will find the name box. It shows the selected cell.

The three types of data you can enter into a cell are data, labels and formulas.

• Data – values, usually numbers but can be letters or a combination of both.
• Labels – headings and descriptions to make the spreadsheet easier to understand.
• Formulas – calculations that update automatically if referenced data changes.

Sorting cell data

The A-Z feature automatically orders data in ascending/descending order or alphabetically.

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Data Collection & Sampling

Covers all parts of the GCSE syllabus, including sampling methods (random and stratified sampling). Powerpoint presentation and associated worksheet.

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24th May 2021 Flag Comment

Very good resource. Thank you very much

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16th May 2018 Flag Comment

Really Good

15th Jan 2018 Flag Comment

very nice and helpful resources.

13th Jan 2018 Flag Comment

Really useful!!

Very nice! Helped me a lot with my CAT

9th Jan 2018 Flag Comment

slides are amazing!

22nd Dec 2017 Flag Comment

these resources are great for revising

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c'est incroyable

28th Dec 2016 Flag Comment

Hi Sir, there is a mistake on slide 14. There is meant to be 2 elephants sampled.

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Awesome resource, only the best teacher

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Thank you for sharing these great resources.

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Sorry, we don't do GCSE Stats.

3rd Aug 2016 Flag Comment

Do you teach GCSE Statistics in your school. If you do, it would be greatful if you could upload some lesson resources. Thanks

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Representing Data

Here we will learn about representing data, including how to create and interpret the different tables, charts, diagrams and graphs we can use to represent data.

There are also representing data worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What is representing data?

Representing data allows us to display and interpret collected data.

Different types of data need to be represented in different formats so we need to know how to construct different types of tables, charts, diagrams or graphs.

Here are some of the charts and graphs you may come across.

Tally charts

A tally chart is a simple way to organise data.

Tally charts can be used for different types of data.

For example,

20 students were asked about their favourite sport. Here are their answers.

Here are these results in a tally chart.

Step-by-step guide: Tally charts

A pictograph (or pictogram) is a chart which uses a symbol to represent a certain frequency. This is then used in a chart.

For example, here is a pictogram to show the number of parcels an office sends in a week.

A full circle represents 4 parcels. So, a semi-circle represents 2 parcels and so on.

Step-by-step guide: Pictograph

Stem and leaf diagram

A stem and leaf diagram organises numerical data into groups, but also retains the value of each piece of data. We can then analyse the data in more depth and find the mode, or the median, and so on.

Here is a stem and leaf diagram for the heights of children.

We can see that the smallest child is 137 \ cm and the tallest child is 165 \ cm. This means we can calculate the range of the data by subtracting the lowest value from the highest value.

Range =165-137=18 \ \text{cm}

Step-by-step guide: Stem and leaf diagram

x and y axis

Many statistical graphs need a pair of axes drawn to start the graph. The x -axis is the name of the horizontal axis and the y -axis is the name of the vertical axis. Care needs to be taken with the scale on the axes. For statistics the x -axis and the y -axis are given different labels.

Here is a bar chart to show the gender of people working in a company. For this bar chart the y axis becomes frequency (f) and the x -axis has the label “gender”.

Step-by-step guide: x and y axis

A bar chart represents data by using vertical (or horizontal) bars of equal width. They are used for categorical or discrete numerical data.

Bar charts can become more complicated and extend to comparative bar charts or compound bar charts (or stacked bar charts).

For example, 

Here is a comparative bar chart showing the favourite pets of boys and girls in a class.

Step-by-step guide: Bar charts

Scatter graphs

Scatter graphs are used to represent bivariate data (two variables). This is when data occurs in pairs of values. The data is plotted on a pair of axes as coordinates.

Scatter graphs can be used to comment about correlation, the relationship between the two variables.

A line of best fit can be drawn through the data and used to help estimate a missing value.

Here is a scatter graph showing the Maths and English scores of a group of students. There is a positive correlation. A line of best fit has been drawn and is being used to estimate a missing English score.

Step-by-step guide: Scatter graphs

Two way tables

Two way tables are a type of table used to organise more complex data where there are two aspects which need to be looked at.

For example, here is a two way table to represent whether people in an office drink tea, or coffee, or neither. Whether the person is male or female is also seen in the table.

Step-by-step guide: Two way tables

A pie chart is a chart with a visual representation of all items of data within a data set using a circle. The sectors of a pie chart are proportional to the different items in the data set. Pie charts are used to represent categorical data.

For example, here is a pie chart to show the favourite type of music.

Step-by-step guide: Pie charts

This is sometimes called a time series graph. Data is plotted on a pair of axes and the points connected by line segments.

For example, a line graph showing sales over a week.

Step-by-step guide: Line graph

Vertical line diagram

A vertical line diagram is very similar to a bar chart. Vertical lines are used instead of bars.

For example, a vertical line diagram to show the shoe sizes of pupils in a dance school.

Time series graph

A time series graph is a line graph which shows data over a given time period. They can be used to show a trend in the data and are useful for making predictions about the future.

The horizontal axis is always used to show the time. The vertical axis represents the variable being recorded against time.

For example, a time series graph showing average temperature over two years. The years are split up into quarters.

Step-by-step guide: Times series graph

Frequency polygon

A frequency polygon is a graph that shows the frequencies of grouped data. The points are plotted using the midpoints of the class intervals against the frequencies and then the points are joined up with straight lines.

Here is the frequency table showing the results of a History test.

Here is the frequency polygon showing the results of the History test.

Step-by-step guide: Frequency polygon

Frequency diagram

Frequency diagrams are usually bar charts, vertical line diagrams or frequency polygons with frequency displayed on the vertical axis.

Step-by-step guide: Frequency diagram

Frequency graphs

Frequency graphs include the charts mentioned in frequency diagrams. But, it also extends to including more complex graphs such as cumulative frequency graphs and histograms.

Step-by-step guide: Frequency graphs

A histogram is used to represent continuous numerical data. They look like bar charts, but they are different. In a bar chart, the heights of the bars represent the frequencies, whereas in a histogram the area of the bars represent the frequencies.

The vertical axis is labelled with frequency density.

The widths of the bars are usually different.

For example, here is a histogram representing the heights of samplings.

The frequency of the first bar is 20 \times 1=20. This means that 20 saplings were between 0 and 20 \ cm tall.

Step-by-step guide: Histograms

Cumulative frequency

Cumulative frequency is the running total of frequencies in a frequency distribution. It can be used to draw a cumulative frequency graph which is useful for representing or analysing the distribution of a large grouped data set.

Cumulative frequency is closely linked to box plots too.

Cumulative frequency can also be used to find estimates for the median value and quartiles of a data set.

For example, here is a cumulative frequency graph for the mass of apples produced by 200 apple trees.

The estimate of the median is 36kg.

Step-by-step guide: Cumulative frequency

A box plot is a diagram showing the following information for a set of data,

• Lowest value (or smallest value)
• Lower quartile
• Upper quartile
• Highest value (or largest value)

They are useful as they show the overall distribution of the data. They can be used to compare one or more sets of data.

For example, here is a box plot showing the amount of money shoppers spend in a local supermarket.

The median is £15.

Step-by-step guide: Box plots

How to represent data

In order to represent data:

Tip 1 Check the type of table, chart, diagram or graph.

Tip 2 Check labels, keys and titles.

Tip 3 Check the scale.

Tip 4 Be as accurate as you can.

Explain how to represent data

Representing data worksheet

Get your free representing data worksheet of 20+ questions and answers. Includes reasoning and applied questions.

Representing data examples

Example 1: tally charts.

Complete the frequencies for the tally chart below.

1 Check the type of table, chart, diagram or graph.

This is a tally chart.

4 Be as accurate as you can.

Be careful counting the tally marks.

This means 5,

Example 2: stem and leaf diagram

Members of a running club were asked their age. Their ages are in this stem and leaf diagram. Write down the mode of their ages.

Check the type of table, chart, diagram or graph.

This is a stem and leaf diagram.

Check labels, keys and titles.

There is a key, which is needed to help us write down the correct age for the mode.

The mode of the ages of the people in the running club is 27 years.

Example 3: scatter graph

Here is a scatter graph. Clive was ill and missed paper 1. He scored 60 on paper 2.

Use the scatter graph and line of best fit to estimate the score on paper 1.

This is a scatter graph. It shows the relationship with bivariate data. The pairs of data are the scores on Paper 1 and Paper 2.

The horizontal axis is for Paper 1 scores and the vertical axis is for Paper 2 scores.

Check the scale.

The scale on both axes are different.

Be as accurate as you can.

Draw a straight line across from 60 on Paper 2. Then go straight down and read off the value for Paper 1.

The estimated score on Paper 1 for Clive is 30 marks.

Example 4: pie chart

24 pupils were asked which subject was their favourite subject. Here is a pie chart to show the results. Work out how many pupils said Science was their favourite subject.

This is a pie chart, so the size of the sector represents the proportion of pupils who chose the different subjects as their favourite.

We need the Science section.

The Science section is a right-angle, so a quarter of the pupils.

So 6 pupils chose Science.

Example 5: two way tables

Complete the two way table.

This is a two way table. We need to look at the column totals and the row totals. We look at a row (or a column) and find 1 missing value to fill in. We could start with the bottom row.

Example 6: frequency polygon

A vet weighs all the dogs she sees in a week. Here are the results.

Draw a frequency polygon to show the results.

We need to draw a frequency polygon. We need to use the midpoints of the groups, 5, 15, 25 and so on.

Frequency is on the vertical axis and mass is on the horizontal axis.

There are two axes, both with different scales, so be careful plotting the points.

Plot points with a sharp pencil and crosses to be accurate. Join the points up to complete the frequency polygon.

Common misconceptions

• Use a pencil, a ruler and a protractor

When drawing graphs, diagrams and charts use a sharp pencil and a ruler so that you can be as accurate as possible. For pie charts, use a protractor to measure the angles accurately.

• Lines of best fit are straight

In GCSE maths the lines of best fit on scatter graphs are a straight line.

• Check the scale

Check the scale and how it is broken up into smaller sections. Scales can come in a variety of styles.

Here is 0 to 100 split up into 10 equal sections, 5 equal sections and 4 equal sections.

Practice representing data questions

1.  Which of these tally charts is NOT correct?

Remember that tally marks are grouped together in 5’s. Check that the frequencies match the number of tally marks.

2. What is the mode?

The value 157 \ cm occurs twice. Therefore the mode is 157.

3. Which type of correlation does this scatter graph show?

Negative correlation

Positive correlation

Inverse correlation

No correlation

There is a downward trend in the plots. This shows there is negative correlation.

4. Which pie chart represents the data in this frequency table?

The total of the frequencies is 40. The frequency of A is 10, which is a quarter of 40. So, section A needs to be a quarter of the pie chart. Similarly section C needs to be a quarter too.

The frequency of B is 20, which is half of 40. Section B needs to be half of the pie chart.

5. Complete the two way table.

Check the rows and columns for a missing value. We could start with finding the missing value for Class X and Spanish,

Then continue to fill in the missing values.

We can also check the column totals and the row totals to check if they are correct.

6. Which of these is the correct frequency polygon for the frequency table below?

The points should be plotted using the midpoints of the groups: 10, 30, 50, 70 and 90.

They should be plotted using the correct frequencies: 1, 9, 8, 3 and 2.

The points need joining up, but NOT the last and the first points.

Representing data GCSE questions

1. Sam has drawn this bar chart. Give two criticisms of the bar chart.

For a valid criticism of the scale. For example, the scale on the vertical axis is missing the number 3.

For a valid criticism about the widths of the bars. For example, the bar for lemonade is too wide.

2. Ali conducts a survey on how long students spend on their maths homework in a week. Here are the results.

Draw a frequency polygon for the information in the table.

For plotting 3 or 4 points correctly.

For all points plotted correctly and joining up the points correctly.

3. Shelia spends £1440 each month running her household. Her household costs can be broken up into food, bills and rent.

(a) Work out how much money Sheila spends on food a month.

(b) Work out how much more money Sheila spends on rent than bills each month.

For using the right angle as a quarter. For example, 1440 \div 4.

For finding the angle for rent. For example, 360-90-120=150.

For finding the difference in angles between rent and bills. For example, 150-120=30.

For finding the proportion of the total costs. For example, \frac{30}{360} \times 1440.

Alternative Method:

For finding the proportion for bills, \frac{120}{360} \times 1440=480 \ OR rent, \frac{150}{360} \times 1440=600.

For finding the difference in money between rent and bills, 600-480.

Learning checklist

You have now learned how to:

• Construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data
• Interpret and construct tables and line graphs for time series data
• Use and interpret scatter graphs of bivariate data; recognise correlation and draw estimated lines of best fit
• Construct and interpret diagrams for grouped discrete data and continuous data, i.e. histograms with equal and unequal class intervals and cumulative frequency graphs, and know their appropriate use

The next lessons are

• Frequency table
• Mean, median, mode
• Types of sampling method

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• Choosing the Right Statistical Test | Types & Examples

Choosing the Right Statistical Test | Types & Examples

Published on January 28, 2020 by Rebecca Bevans . Revised on June 22, 2023.

Statistical tests are used in hypothesis testing . They can be used to:

• determine whether a predictor variable has a statistically significant relationship with an outcome variable.
• estimate the difference between two or more groups.

Statistical tests assume a null hypothesis of no relationship or no difference between groups. Then they determine whether the observed data fall outside of the range of values predicted by the null hypothesis.

If you already know what types of variables you’re dealing with, you can use the flowchart to choose the right statistical test for your data.

Statistical tests flowchart

Table of contents

What does a statistical test do, when to perform a statistical test, choosing a parametric test: regression, comparison, or correlation, choosing a nonparametric test, flowchart: choosing a statistical test, other interesting articles, frequently asked questions about statistical tests.

Statistical tests work by calculating a test statistic – a number that describes how much the relationship between variables in your test differs from the null hypothesis of no relationship.

It then calculates a p value (probability value). The p -value estimates how likely it is that you would see the difference described by the test statistic if the null hypothesis of no relationship were true.

If the value of the test statistic is more extreme than the statistic calculated from the null hypothesis, then you can infer a statistically significant relationship between the predictor and outcome variables.

If the value of the test statistic is less extreme than the one calculated from the null hypothesis, then you can infer no statistically significant relationship between the predictor and outcome variables.

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You can perform statistical tests on data that have been collected in a statistically valid manner – either through an experiment , or through observations made using probability sampling methods .

For a statistical test to be valid , your sample size needs to be large enough to approximate the true distribution of the population being studied.

To determine which statistical test to use, you need to know:

• whether your data meets certain assumptions.
• the types of variables that you’re dealing with.

Statistical assumptions

Statistical tests make some common assumptions about the data they are testing:

• Independence of observations (a.k.a. no autocorrelation): The observations/variables you include in your test are not related (for example, multiple measurements of a single test subject are not independent, while measurements of multiple different test subjects are independent).
• Homogeneity of variance : the variance within each group being compared is similar among all groups. If one group has much more variation than others, it will limit the test’s effectiveness.
• Normality of data : the data follows a normal distribution (a.k.a. a bell curve). This assumption applies only to quantitative data .

If your data do not meet the assumptions of normality or homogeneity of variance, you may be able to perform a nonparametric statistical test , which allows you to make comparisons without any assumptions about the data distribution.

If your data do not meet the assumption of independence of observations, you may be able to use a test that accounts for structure in your data (repeated-measures tests or tests that include blocking variables).

Types of variables

The types of variables you have usually determine what type of statistical test you can use.

Quantitative variables represent amounts of things (e.g. the number of trees in a forest). Types of quantitative variables include:

• Continuous (aka ratio variables): represent measures and can usually be divided into units smaller than one (e.g. 0.75 grams).
• Discrete (aka integer variables): represent counts and usually can’t be divided into units smaller than one (e.g. 1 tree).

Categorical variables represent groupings of things (e.g. the different tree species in a forest). Types of categorical variables include:

• Ordinal : represent data with an order (e.g. rankings).
• Nominal : represent group names (e.g. brands or species names).
• Binary : represent data with a yes/no or 1/0 outcome (e.g. win or lose).

Choose the test that fits the types of predictor and outcome variables you have collected (if you are doing an experiment , these are the independent and dependent variables ). Consult the tables below to see which test best matches your variables.

Parametric tests usually have stricter requirements than nonparametric tests, and are able to make stronger inferences from the data. They can only be conducted with data that adheres to the common assumptions of statistical tests.

The most common types of parametric test include regression tests, comparison tests, and correlation tests.

Regression tests

Regression tests look for cause-and-effect relationships . They can be used to estimate the effect of one or more continuous variables on another variable.

Comparison tests

Comparison tests look for differences among group means . They can be used to test the effect of a categorical variable on the mean value of some other characteristic.

T-tests are used when comparing the means of precisely two groups (e.g., the average heights of men and women). ANOVA and MANOVA tests are used when comparing the means of more than two groups (e.g., the average heights of children, teenagers, and adults).

Correlation tests

Correlation tests check whether variables are related without hypothesizing a cause-and-effect relationship.

These can be used to test whether two variables you want to use in (for example) a multiple regression test are autocorrelated.

Non-parametric tests don’t make as many assumptions about the data, and are useful when one or more of the common statistical assumptions are violated. However, the inferences they make aren’t as strong as with parametric tests.

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This flowchart helps you choose among parametric tests. For nonparametric alternatives, check the table above.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Normal distribution
• Descriptive statistics
• Measures of central tendency
• Correlation coefficient
• Null hypothesis

Methodology

• Cluster sampling
• Stratified sampling
• Types of interviews
• Cohort study
• Thematic analysis

Research bias

• Implicit bias
• Cognitive bias
• Survivorship bias
• Availability heuristic
• Nonresponse bias
• Regression to the mean

Statistical tests commonly assume that:

• the data are normally distributed
• the groups that are being compared have similar variance
• the data are independent

If your data does not meet these assumptions you might still be able to use a nonparametric statistical test , which have fewer requirements but also make weaker inferences.

A test statistic is a number calculated by a  statistical test . It describes how far your observed data is from the  null hypothesis  of no relationship between  variables or no difference among sample groups.

The test statistic tells you how different two or more groups are from the overall population mean , or how different a linear slope is from the slope predicted by a null hypothesis . Different test statistics are used in different statistical tests.

Statistical significance is a term used by researchers to state that it is unlikely their observations could have occurred under the null hypothesis of a statistical test . Significance is usually denoted by a p -value , or probability value.

Statistical significance is arbitrary – it depends on the threshold, or alpha value, chosen by the researcher. The most common threshold is p < 0.05, which means that the data is likely to occur less than 5% of the time under the null hypothesis .

When the p -value falls below the chosen alpha value, then we say the result of the test is statistically significant.

Quantitative variables are any variables where the data represent amounts (e.g. height, weight, or age).

Categorical variables are any variables where the data represent groups. This includes rankings (e.g. finishing places in a race), classifications (e.g. brands of cereal), and binary outcomes (e.g. coin flips).

You need to know what type of variables you are working with to choose the right statistical test for your data and interpret your results .

Discrete and continuous variables are two types of quantitative variables :

• Discrete variables represent counts (e.g. the number of objects in a collection).
• Continuous variables represent measurable amounts (e.g. water volume or weight).

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Bevans, R. (2023, June 22). Choosing the Right Statistical Test | Types & Examples. Scribbr. Retrieved September 13, 2023, from https://www.scribbr.com/statistics/statistical-tests/

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Types of Data

Subject: Mathematics

Age range: 11-14

Resource type: Lesson (complete)

Last updated

22 February 2018

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