CIMA BA1 Syllabus C. Informational Context Of Business - Histograms - Notes ^{5 / 7}

Histograms and frequency distributions

Frequency distribution

A frequency distribution shows how often each different value occurs.

A histogram is the most commonly used graph to show frequency distributions.

Illustration: A histogram with EQUAL intervals

The table below shows how many hours students study per week.

Hours Spent to study	Number of Students (Frequency)
0 - 1	10
1 - 1.99	15
2 - 2.99	4
3 - 3.99	3
4 - 4.99	1

Interpreting a histogram with unequal class intervals

If a distribution has unequal intervals, the heights of the bars have to be adjusted for the fact that the bars do not have the same width.

With a histogram we look at the whole area (not just a height), also a width.

Illustration: A histogram with UNEQUAL intervals

The table below shows how many hours students study per week.

Number of Hours	Number of students
> 3 ≤ 5	8
> 5 ≤ 6	6
>6 ≤ 8	6
>8 ≤ 10	10
>10 ≤ 13	6

Note the symbol:
≤ means 'less than or equal to'.
> means 'greater than'

Here the class intervals for hours are not all the same

1 (eg 5 - 6)
2 (eg 6 - 8)
3 (eg 10 - 13)

So a bar chart would be misleading because there will naturally be more students in the bigger intervals than the smaller intervals.

That's why we use a Histogram.

A histogram is drawn as follows:

Choose a standard width of bar
This will be the most frequently occurring interval
in Our Illustration this is an interval of 2.
The width of each bar on the chart reflects the size of the interval
eg > 6 ≤ 8 , a range of 2, will be twice as wide as the bar representing > 5 ≤ 6, a range of 1.
Calculate the height of the bar
Check the adjustment in the following table:

Number of Hours	Size of interval	Number of students (Frequency)	Adjustment	Height of bar
> 3 ≤ 5	2	8	x 2/2	8
> 5 ≤ 6	1	6	x 2/1	12
>6 ≤ 8	2	6	x 2/2	6
>8 ≤ 10	2	10	x 2/2	10
>10 ≤ 13	3	6	x 2/3	4