Part 7:
Statistical Calculations

Example 7.3a

Here we see the wages of a set of employees, grouped in intervals of £50 (apart from the last one):

Wages (£)
100-150
150-200
200-250
250-300
300-350
350-400
400-500
Frequency (f)
17
25
34
47
26
15
3


Find the mean and standard deviation.

Solution:
The first interval thus emcompasses all wages between £100.00 and £149.99. A wage of £150.00 is included in the second interval.

Consider the first interval. The 17 employees could all be earning as much as £149.99 each or as little as £100.00 each, we have no way of knowing. So, in order to make any calculations at all, we have to make a fairly big assumption - that they all earn an amount slap-bang in the middle of the interval, i.e. (100 + 150) ÷ 2 = £125.

The table now looks like this, the second row (our x column) being the mid-values of each interval. That the last inverval is different makes no odds, our last mid-value just looks a bit different from the rest as well.

The calculations now follow:
 Wages
Mid Value x
f
fx
fx2
100-150
125
17
2,1150.0
268,750.00
150-200
175
25
4,375.0
765,625.00
200-250
225
34
7,650.0
1,721,250.00
250-300
275
47
12,925.0
3,554,375.00
300-350
325
26
8,450.0
2,746,250.00
350-400
375
15
5,625.0
2,109,375.00
400-500
450
3
1,350.0
607,500.00
 Totals
 
167
42,525.0
11,773,125.00
 


The mean wage of this group of employees is £254.49 per week, and the wages are spread about so that, on average, the wages are £75.59 away from the mean.
The real mean and standard deviation will be a bit different, of course, but these figures will be close enough to be used in any further calculations or discussions.