# Histograms

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

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

This is level 2: read information from histograms 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 length of snakes in Zoofield Safari Park. How many snakes have lengths between 120cm and 150cm? 30 60 90 120 150 180 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - Lengths of snakes in centimetres 2) The Flint Book Club has many members between the ages of twenty and sixty. The spread of ages is shown in this histogram. What is the total number of people in the book club? 20 25 30 35 40 45 50 55 60 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - Ages of Book Club Members 3) Mrs Bitfit keeps a record of how many steps she has walked each day. The histogram shows the data she has collected so far. On how many days did she walk more than 7000 steps? 0 1 2 3 4 5 6 7 8 9 10 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - Number of steps per day in thousands 4) The fish in a remote lake were weighed and the data is shown in the histogram below. Estimate the total weight of all the fish in the 250g to 300g range. Give your answer in grams. 100 150 200 250 300 350 400 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - Weights of fish in grams 5) The histogram below shows the speed of cars driving through a dangerous bend one evening. Calculate an estimate of the average (mean) speed of all the cars giving your answer correct to the nearest whole number. 0 10 20 30 40 50 60 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - Speeds of cars in kilometers per hour
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This is Histograms level 2. You can also try:
Level 1 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.

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When planning to use technology in your lesson always have a plan B!

Ella Chandler, England

Saturday, December 11, 2021

"Level 1 and 2 of the 'Histogram' activity are incorrect, they show and ask questions about bar charts but refer to them as histograms when the y-axis is clearly labelled frequency, not frequency density. This is a shame as I find these activities very useful with my students and am sad to not have an activity I can with them for this topic.

[Transum: Thank you for your feedback Ella. The definitions of a histogram that I have read do not stipulate that the y-axis should represent frequency density unless the groups (bins) are not all the same width.]"

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© Transum Mathematics :: This activity can be found online at:
www.Transum.org/go/?Num=820

## 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).

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## 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.

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