The contents of 100 matchboxes 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 upto exactly 39 matches.

(i) We construct the following table:

Mean = $\dfrac{∑f$ixi}{∑f_i} = \dfrac{3813}{100} = 38.1

Hence, the mean of number of matches per box is 38.1

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

Let the no. of matches added to total contents of 100 boxes be x in order to bring mean to 39. So, total matches becomes 3813 + x.

$\therefore 39 = \dfrac{3813 + x}{100} \\[1em] \Rightarrow 3900 = 3813 + x \\[1em] \Rightarrow x = 3900 - 3813 = 87.$

Hence, 87 extra matches need to added to bring the mean upto exactly 39 matches.