The mean of the numbers a, b, 8, 5, 10 is 6 and their variance is 6.8.

Question

The mean of the numbers a, b, 8, 5, 10 is 6 and their variance is 6.8. If M is the mean deviation of the numbers about the mean, then $25M$ is equal to:

Accepted Answer

Mean $=6$: $a+b+8+5+10=30 \implies a+b=7$

Variance $=6.8$: $\dfrac{(a-6)^2+(b-6)^2+4+1+16}{5}=6.8 \implies (a-6)^2+(b-6)^2=13$

Solving together with $a+b=7$ gives $a=3, b=4$ (or vice versa) --- consistent with the known companion problem (Question 151) using the same five numbers.

Data: $3,4,8,5,10$; mean $=6$.

$$M = \frac{|3-6|+|4-6|+|8-6|+|5-6|+|10-6|}{5} = \frac{3+2+2+1+4}{5} = \frac{12}{5}=2.4$$

$$25M = 25\times2.4 = 60$$

Solutions · 1