9. Find the mean, variance and standard deviation using short-cut method.
Height in cms | 70-75 | 75-80 | 80-85 | 85-90 | 90-95 | 95-100 | 100-105 | 105-110 | 110-115 |
No. of students | 3 | 4 | 7 | 7 | 15 | 9 | 6 | 6 | 3 |
Let the assumed mean, A = 92.5 and h = 5
Height in cms |
Frequency
|
Midpoint
|
||||
70-75 | 3 | 72.5 | -4 | 16 | -12 | 48 |
75-80 | 4 | 77.5 | -3 | 9 | -12 | 36 |
80-85 | 7 | 82.5 | -2 | 4 | -14 | 28 |
85-90 | 7 | 87.5 | -1 | 1 | -7 | 7 |
90-95 | 15 | 92.5 | 0 | 0 | 0 | 0 |
95-100 | 9 | 97.5 | 1 | 1 | 9 | 9 |
100-105 | 6 | 102.5 | 2 | 4 | 12 | 24 |
105-110 | 6 | 107.5 | 3 | 9 | 18 | 54 |
110-115 | 3 | 112.5 | 4 | 16 | 12 | 48 |
=N = 60 |
|
= 6 |
=254 |
Mean,
We know, Variance,
We know, Standard Deviation =
Hence, Mean = 93, Variance = 105.583 and Standard Deviation = 10.275