ACCA MA · Guided practice (Show me how)
Chapter 22: Measures of Average and of Dispersion
Averages and dispersion - the middle, and the spread around it
An average on its own can be misleading: two sets of figures with the same mean can look completely different. So we calculate an average, and then a measure of how far the observations sit from it.
Part (a) - discrete data. A company has recorded the number of complaints received per week over the past thirteen weeks.
| Number of complaints | Frequency |
|---|---|
| 0 | 1 |
| 1 | 6 |
| 2 | 4 |
| 3 | 2 |
| 13 |
The total of the squared differences, SUM f(X - mean) squared, is 9.21.
Part (b) - grouped data. The same company has recorded the total amount paid to employees each week over the last year.
| Total paid ($) | Frequency |
|---|---|
| 0 - under 500 | 1 |
| 500 - under 1,000 | 4 |
| 1,000 - under 1,500 | 8 |
| 1,500 - under 2,000 | 19 |
| 2,000 - under 2,500 | 14 |
| 2,500 - under 3,000 | 6 |
| 52 |
Grouped data no longer records the individual figures, so each class is represented by its MID-POINT. Using the mid-points, SUM f(X - mean) squared = 17,514,428.
(a) Discrete data
Calculate the mean, the median, the mode, the range, the variance, the standard deviation and the coefficient of variation of the number of complaints received per week.
(b) Grouped data
Calculate the mean, the variance, the standard deviation and the coefficient of variation of the weekly wages paid.
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