Prove by an example that the variance is unaffected by the choice of the assumed mean.
We take the following example for proving that the variance is uneffected by the choice of the assumed mean.
Example : Calculate variance of 25, 50, 45, 30, 70, 42, 36, 48, 34 and 60 by actual mean assumed mean method.
(a) Calculation of Variance by Actual Mean Method
|
Values of X |
|
x2 |
|
25 |
–19 |
361 |
|
50 |
+6 |
36 |
|
45 |
+1 |
1 |
|
30 |
–14 |
196 |
|
70 |
–26 |
676 |
|
42 |
–2 |
4 |
|
36 |
–8 |
64 |
|
48 |
+4 |
16 |
|
34 |
–10 |
100 |
|
60 |
+16 |
256 |
|
ΣX = 440 |
ΣX2 = 1710 |
(b) Calculation of Variance by Assumed Mean Method
|
Values X |
(X–45) d |
d2 |
|
25 |
–20 |
400 |
|
50 |
+5 |
25 |
|
45 |
0 |
0 |
|
30 |
–15 |
225 |
|
70 |
+25 |
625 |
|
42 |
–3 |
9 |
|
36 |
–9 |
81 |
|
48 |
+3 |
9 |
|
34 |
–11 |
121 |
|
60 |
+15 |
225 |
|
N=10 |
Σd = –10 |
Σd2 =1720 |
(x)
