Class interval | fi | xi | ui=xi−Ah | u2i | fiui | fiu2i |
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 |
Total | 60 | | | | 6 | 254 |
We have N=∑fi=60 Width of class h=5
Assumed mean A=92.5(say)
Mean, ¯x=A+∑9i=1fiuiN×h
=92.5+660×5=92.5+0.5=93
⇒¯x=93
Variance σ2=h2⎡⎣∑9i=1fiu2iN−(∑9i=1fiuiN)2⎤⎦
σ2=52[25460−(660)2]
=52[60×254−62](60)2
=253600[15240−36]
=253600×15204
σ2=105.58
Standard Deviation =√Variance
σ=√105.58
σ=10.27