# Histograms

## Practise drawing and reading information from histograms displaying grouped data

##### Level 1Level 2Level 3Level 4Level 5Exam-StyleDescriptionHelpMore Statistics

This is level 1: show the height of one bar in an almost-complete histogram with fixed class intervals. You can earn a trophy if you get at least 4 questions correct and you do this activity online.

1) This histogram shows the height of sunflowers in Julie's garden. Drag the first bar to show a frequency of 7 for the shortest group of sunflowers.

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Heights of sunflowers in centimetres

2) In an animal sanctuary the birds were weighed and the data is shown in the histogram below. There were 8 birds weighing between 450g and 500g. Adjust the height of the last bar of this histogram to show this information.

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Weights of birds in grams

3) This table and histogram below show the speed of cars passing Julie's house one morning. Drag the third bar to show the frequency of cars travelling between twenty and thirty miles per hour.

 Speed (s) mph 0 < s ≤ 10 10 < s ≤ 20 20 < s ≤ 30 30 < s ≤ 40 40 < s ≤ 50 50 < s ≤ 60 Number of cars 4 9 5 12 9 12

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Speeds of cars in miles per hour

4) The Friday Allotment Coffee Club has exactly 41 members between the ages of twenty and a hundred. Drag the bar for the 70 to 80 age group to complete the histogram.

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Ages of Club Members

5) Jason keeps a record of how many kilometers he cycles each day. The histogram shows the data he has collected so far. He was surprised to realise that on a total of 29 days he cycled more than 21 kilometres. Adjust the height of the last bar of the histogram to show this information.

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Distance cycled in kilometres

Check

This is Histograms level 1. You can also try:
Level 2 Level 3 Level 4 Level 5

## Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

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## Description of Levels

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Reading Graphs and Charts - Answer real-life problems from different types of graphs and charts including piece-wise linear graphs.

Level 1 - Show the height of one bar in an almost-complete histogram with fixed class intervals

Level 2 - Read information from histograms with fixed class intervals

Level 3 - Complete a frequency table with information from a histogram with unequal class intervals

Level 4 - Complete a frequency table with information from a histogram showing frequency density

Level 5 - General questions about histograms with varying class widths

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

## Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

## Histograms

Histograms are similar to bar charts but there is one important difference. It is the area of the bars in a histogram that is proportional to the frequency rather than the height.

The first couple of levels of this exercise features histograms with equal class widths which means the heights of the bars can be conveniently used to find the frequency.

Levels 3 onwards contain histograms with unequal class widths so the vertical axis can be thought of as the frequency density.

Frequency = Frequency density × Class Width

Histograms can be used to represent both discrete and continuous data but they are typically used for displaying continuous data.

To draw a histogram, the data first needs to be assigned to a number of different groups (classes or bins). There are various theories concerning how many of these groups there should be but the normal is between five and twenty depending on the amount of data. A number of consecutive groups containing very little data may be merged into a single group.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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