The contents of 100 match boxes were checked to determine the number of matches they contained.

No. of matches	No. of boxes
35	6
36	10
37	18
38	25
39	21
40	12
41	8

(i) Calculate, correct to one decimal place, the mean number of matches per box.

(ii) Determine, how many extra matches would have to be added to the total contents of the 100 boxes to bring the mean up to exactly 39 matches ?

(i)

By formula,

Mean = $\dfrac{Σfx}{Σf} = \dfrac{3813}{100}$ = 38.13 ≈ 38.1

Hence, mean = 38.1

(ii) By formula,

Mean = $\dfrac{\text{No. of matches}}{\text{No. of boxes}}$

If mean = 39.

$\Rightarrow 39 = \dfrac{\text{No. of matches}}{100} \\[1em] \Rightarrow \text{No. of matches} = 3900$

No. of matches to add = 3900 - 3813 = 87.

Hence, 87 extra matches need to be added.