Class | fi | xi | ui=xi−Ah | u2i | fiui | fiu2i |
10-20 | 9 | 15 | -3 | 9 | -27 | 81 |
20-30 | 17 | 25 | -2 | 4 | -34 | 68 |
30-40 | 32 | 35 | -1 | 1 | -32 | 32 |
40-50 | 33 | 45 | 0 | 0 | 0 | 0 |
50-60 | 40 | 55 | 1 | 1 | 40 | 40 |
60-70 | 10 | 65 | 2 | 4 | 20 | 40 |
70-80 | 9 | 75 | 3 | 9 | 27 | 81 |
Total | 150 | | | | -6 | 342 |
Here h=10,N=150Let assumed mean A=45
Mean ¯x=A+∑7i=1fiuiN×h
=45+(−6)×10150=45−0.4=44.6
Variance (σ21)=h2N2⎡⎣N7∑i=lfiu2i−(7∑i=lfiui)2⎤⎦
=10022500[150×342−(6)2]
=1225(51264)
=227.84
∴ Standard deviation (σ1)=√227.84=15.09
Group B:
Class | fi | xi | ui=xi−Ah | u2i | fiui | fiu2i |
10-20 | 10 | 15 | -3 | 9 | -30 | 90 |
20-30 | 20 | 25 | -2 | 4 | -40 | 80 |
30-40 | 30 | 35 | -1 | 1 | -30 | 30 |
40-50 | 25 | 45 | 0 | 0 | 0 | 0 |
50-60 | 43 | 55 | 1 | 1 | 43 | 43 |
60-70 | 15 | 65 | 2 | 4 | 30 | 60 |
70-80 | 7 | 75 | 3 | 9 | 21 | 63 |
Total | 150 | | | | -6 | 366 |
Here h=10,N=150Let assumed mean A=45
Mean ¯x=A+∑7i=1fiuiN×h
=45+(−6)×10150=45−0.4=44.6
Variance (σ22)=h2N2⎡⎣N7∑i=lfiu2i−(7∑i=lfiui)2⎤⎦
=10022500[150×366−(6)2]
=1225(54864)
=243.84
∴ Standard deviation (σ2)=√243.84=15.61
Since, the mean of both the groups is same the group with greater standard deviation will be more variable.
Thus group B has more variability in the marks.