The number of match sticks contained in 50 match boxes is given below :

Number of match sticks	Number of boxes
40	6
42	7
43	12
44	9
45	10
48	6

(i) Using short cut method, find the mean number of match sticks per box.

(ii) How many extra match sticks are to be added to all the contents of 50 match boxes to bring the mean exactly equal to 45 match sticks per box?

(i) We know that,

n = ∑f = 50.

By formula,

$\text{Mean} = A + \dfrac{\sum fd}{n} \\[1em] = 44 + \dfrac{-16}{50} \\[1em] = 44 - 0.32 \\[1em] = 43.68$

Hence, mean number of match sticks per box is 43.68

(ii) Total number of sticks = Mean × Total Boxes

= 43.68 × 50

= 2184 sticks

Number of match sticks to be added = (50 × 45) − 2184 = 66.

Hence, extra match sticks to be added = 66.