Part 7:
Statistical Calculations

Data in the Form of a Simple Frequency Table

We have to amend our formulae slightly.


Example 7.2

Here we have the number of strokes required by golfers to get round a particular course one day:

No. of Strokes (x)
67
68
69
70
71
72
73
74
75
No. of Golfers(f)
15
23
38
27
25
19
16
10
4


Find the mean and the standard deviation.

Solution:

How do we apply the formulae to the table?

We start by writing the data in a column, not a row, and adding a column for fx and another column for fx².

Note that fx means f × x and that fx² means either fx × x or f × x² but emphatically NOT fx × fx.

Thus the formula for the mean states '(total number of strokes) ÷ (total number of golfers)' giving us the average number of strokes per golfer.

You need some fairly complicated maths to see that the formula for the standard deviation calculates the same thing as the first formula did on page 7, but please take my word for it that it does.

x f fx fx2
67
15
1,005
67,335
68
23
1,564
106,352
69
38
2,622
180,918
70
27
1,890
132,300
71
25
1,775
126,025
72
19
1,368
98,496
73
16
1,168
85,264
74
10
740
54,760
75
4
300
22,500
Totals
177
12,432
873,950


Thus the first line reads:
15 golfers scored 67. This makes a total of 15 × 67 = 1,005 strokes. The 67,335 we get by multiplying 1,005 by 67, alternatively, 15 × 67 × 67 or 15 × 67².

Other lines you get in a similar way. Then find the total for each column.