Question

The number of inquiries received by a school on administration each day are recorded as: 40, 43, 49, 45, 46, 42, 43. Find the variance in the inquires per day

Answer 1

$$\bar{x}=\dfrac{40+43+49+45+46+42+43}{7}=44$$

Variance

$$Var(X)=\sigma^2=\dfrac{\Sigma(x_i-\bar{x})^2}{n}$$

$$=\dfrac{1}{7}((40-44)^2+(43-44)^2+(49-44)^2$$

$$+(45-44)^2+(46-44)^2+(42-44)^2$$

$$+(40-44)^2)=\dfrac{9+1+25+1+4+4+16}{7}=\dfrac{60}{7}$$

$$=\dfrac{60}{7}$$