Question

A work-standards expert observes the amount of time required to prepare a sample of 10 business letters in an office with the following results listed in ascending order to the nearest minute: 5, 5, 5, 7, 9, 14, 15, 15, 16, 18. Determine the
Range

Answer 1

(i) $n=10$

$$5,5,5,7,9,14,15,15,16,18$$

$$Range=18-5=13$$

(ii)

$$mean =\dfrac{1}{15}(5+5+5+7+9+14+15+15$$

$$+16+18)=10.9$$

(iii)

$$median=\dfrac{9+14}{2}=11.5$$

(iv)

$$mode=5\ (3\ times)$$

(v)

$$Var(x)=\sigma^2=\dfrac{1}{10}((5-10.9)^2+(5-10.9)^2$$

$$+(5-10.9)^2+(7-10.9)^2+(9-10.9)^2$$

$$+(14-10.9)^2+(15-10.9)^2+(15-10.9)^2$$

$$+(16-10.9)^2+(18-10.9)^2=24.29$$

(vi)

$$\sigma=\sqrt{\sigma^2}=\sqrt{24.29}\approx4.9285$$