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Histogram (Non-Uniform Widths)




 
Related Topics:
More Lessons for Statistics, Math Worksheets

What is a Histogram?
How to interpret and draw a histogram?

When constructing a histogram with non-uniform (unequal) class widths, we must ensure that the areas of the rectangles are proportional to the class frequencies.

Remember that the histogram differs from a bar chart in that it is the area of the bar that denotes the value, not the height. This means that we would need to consider the widths in order to determine the height of each rectangle.

Example

The following frequency distribution gives the masses of 48 objects measured to the nearest gram. Draw a histogram to illustrate the data.

Mass (g)

10 – 19

20 – 24

25 – 34

35 – 50

51 – 55

Frequency

6

4

12

18

8

Solution:

Evaluate each class widths.

Mass (g)

10 – 19

20 – 24

25 – 34

35 – 50

51 – 55

Frequency

6

4

12

18

8

Class width

10

5

10

15

5

Since the class widths are not equal, we choose a convenient width as a standard and adjust the heights of the rectangles accordingly.

We notice that the smallest width size is 5. We can choose 5 to be the standard width. The other widths are then multiples of the standard width.

The table below shows the calculations of the heights of the rectangles.

Mass (g)

10 – 19

20 – 24

25 – 34

35 – 50

51 – 55

Frequency

6

4

12

18

8

Class widths

10

5

10

15

5

2 × standard

standard

2 × standard

3 × standard

standard

Rectangle’s height in histogram

6 ÷ 2 = 3

4

12 ÷ 2 = 6

18 ÷ 3 = 6

8




Histogram with uneven class widths. Higher GCSE topic revision
Understand what is a histogram.
Draw a histogram given some information.
Interpret a histogram.
GCSE Maths - Histograms - Unequal Class Intervals - Frequency Density - Higher A/A* grade
Example 1: The table below shows the length in mm of some worms found in Steve's garden. Draw a histogram to represent the information.
Example 2: The histogram shows the range of ages of members of a spots centre. Complete the frequency table.
Example 3: The histogram gives information about the heights of 540 Christmas trees. Work out an estimate for the number of Christmas trees with a height greater than 3 metres.


 

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.


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