Using short cut method, find the mean, variation and standard deviation for the data :
xi | 4 | 8 | 11 | 17 | 20 | 24 | 32 |
fi | 3 | 5 | 9 | 5 | 4 | 3 | 1 |
To find: MEAN
(xi) | (fi) | xifi |
4 | 3 | 12 |
8 | 5 | 40 |
11 | 9 | 99 |
17 | 5 | 85 |
20 | 4 | 80 |
24 | 3 | 72 |
32 | 1 | 32 |
Total | ∑fi = 30 | ∑fixi =420 |
Now, 
=14
To find: VARIANCE
(xi) | (fi) |
|
|
|
4 | 3 | 4 – 14 = -10 | (-10)2 = 100 | 3 × 100 = 300 |
8 | 5 | 8 – 14 = -6 | (-6)2 = 36 | 5 × 36 = 180 |
11 | 9 | 11 – 14 = -3 | (-3)2 = 9 | 9 × 9 = 81 |
17 | 5 | 17 – 14 = 3 | (3)2 = 9 | 5 × 9 = 45 |
20 | 4 | 20 – 14 = 6 | (6)2 = 36 | 4 × 36 = 144 |
24 | 3 | 24 – 14 = 10 | (10)2 = 100 | 3 × 100 = 300 |
32 | 1 | 32 – 14 = 18 | (18)2 = 324 | 1 × 324 = 324 |
N = 30 |
|
= 45.8
To find: STANDARD DEVIATION
= 6.77
1