Question

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

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

1. Calculate, correct to one decimal place, the mean number of matches per box. 
2. 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.

Answer 1

No. of matches (x)	No. of boxes (f)	fx
35	6	210
36	10	360
37	18	666
38	25	950
39	21	819
40	12	480
41	8	328
Total	100	3813

i. `barx = (sumfx)/(sumf)`

= `3813/100`

= 38.13 

ii. In the second case,

New mean = 39 matches 

Total contents = 39 × 100 = 3900

But total number of matches already given = 3813 

Number of new matches to be added = 3900 – 3813 = 87