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Histograms

Practise drawing and reading information from histograms displaying grouped data

Level 1 Level 2 Level 3 Level 4 Level 5 Exam-Style Description Help More 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.

Histogram
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?

Correct Wrong

2. How many people take less than 20 minutes to get to work?

Correct Wrong

3. What is the frequency of the modal class?

Correct Wrong

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?

Correct Wrong

Histogram
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?

Correct Wrong

6. What is the frequency of the modal class?

Correct Wrong

7. What is the total number of houses in the village?

Correct Wrong

8. What percent of houses have only one occupant? Give your answer to the nearest whole number.

Correct Wrong
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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.

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.

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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.

Histogram

Qwfp at English Wikipedia [CC BY-SA 3.0], via Wikimedia Commons

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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