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# Histograms

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

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

This is level 5: general questions about histograms with varying class widths. You can earn a trophy if you get at least 6 questions correct and you do this activity online.

 The histogram above shows the time taken to comute to work for the employees of a large company.1. How many people take between 35 and 45 minutes to get to work? 2. How many people take less than 20 minutes to get to work? 3. What is the frequency of the modal class? 4. Fifty people from another town join the company. It takes them between 60 and 70 minutes to comute. An extra bar is added to the histogram above. What frequency density will the height of this bar represent? The histogram above was constructed from the data collected about the number of people per house in a rural village. As the data is discrete you will notice that, for example, the class boundaries for two people living in a house are 1.5 and 2.5. The number of houses with three occupants is 20.5. How many houses have five or six occupants? 6. What is the frequency of the modal class? 7. What is the total number of houses in the village? 8. What percent of houses have only one occupant? Give your answer to the nearest whole number.
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This is Histograms level 5. You can also try:
Level 1 Level 2 Level 3 Level 4

## 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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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).

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

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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.

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.

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