Question

Find the variance and standard deviation for the following data.

xi=3 ,6 ,9 ,12 ,13 ,15 ,21 ,22

fi=3 ,4 ,5 ,2, 4, 5 ,4 ,3​

Answer 1

Answer:

Mean =

x

ˉ

=

∑f

i

∑f

i

x

i

=

3+5+9+5+4+3+1

4×3+8×5+11×9+17×5+20×4+24×3+32×1

=

30

12+40+99+85+80+72+32

=

30

420

=14

Variance =

∑f

i

∑f

i

(x

i

−

x

ˉ

)

2

=

30

3(4−14)

2

+5(8−14)

2

+9(11−14)

2

+5(17−14)

2

+4(20−14)

2

+3(24−14)

2

+1(32−14)

2

=

30

300+180+81+45+144+300+324

=

30

1374

=45.8

Standard deviation equals

45.8

=6.767