Question

The contents of 100 match box were checked to determine the number of match sticks they contained.

Number of match sticks	Number 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 match sticks per box.
(ii) Determine how many matchsticks would have to be added. To the total contents of the 100 boxes to bring the mean up exactly 39 match sticks.

Answer 1

Number of match sticks `(x_i)`	Number of boxes `(f_i)`	`f_ix_i`
35	6	210
36	10	360
37	18	666
38	25	950
39	21	819
40	12	480
41	8	328
	`sumf_i` = 100	`sumf_ix_i` = 3813

∴ Mean = `(sumf_ix_i)/(sumf_i) = (3813)/(100)`
= 38·13 ∼ 38·1.
(ii) Now the number of extra sticks to be added.
= 39 x 100 - 38·13 x 100
= 3900 - 3813 = 87.