Question

Take an imaginary example applicable to geographical analysis and explain direct and indirect methods of calculating the mean from ungrouped data.

Answer 1

The annual rainfall (in cm) recorded at 5 weather stations in a district.

Imaginary Dataset (Rainfall in cm): 70, 90, 110, 80, 100

Total number of observations (N): 5

1. Direct Method:

`bar(X) = (sumX)/N`

∑X = 70 + 90 + 110 + 80 + 100

= 450

bar(X) = 450/5`

= 90 cm

The mean annual rainfall using the Direct Method is 90 cm.

2. Indirect Method:

`bar(X) = A + (sumd)/N`

Let the Assumed Mean (A) = 80

Deviation (d = X − 80)

Station	Rainfall (X)	Deviation (d = X − 80)
1	70	70 − 80 = −10
2	90	90 − 80 = 10
3	110	110 − 80 = 30
4	80	80 − 80 = 0
5	100	100 − 80 = 20
Total		∑d = 50

`bar(X) = 80 + 50/5`

`bar(X)` = 80 + 10

`bar(X)` = 90

The mean annual rainfall using the Indirect Method is also 90 cm.