Question

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

Calculate correct to one decimal place the mean number of matches per box; determine how many extra matches would be needed to be added to the total contents of the $100$ boxes to bring the mean to exactly $39$.

• A. 38.1, 86
• B. 38.1, 87
• C. 36.1, 88
• D. 36.1, 90
• E. 35.1, 86

Answer 1

The correct option is E $38.1,87$

$\begin{array}{ccc}\text{No. of matches}{x}_i& \text{No. of matches}{f}_i& x_i{f}_i\\ 35& 6& 210\\ 36& 10& 360\\ 37& 18& 666\\ 38& 25& 950\\ 39& 21& 819\\ 40& 12& 480\\ 41& 8& 328\\ & \sum f_i=100& \sum x_i=3813\end{array}$

Mean $=\frac{\sum f_i{x}_i}{\sum f_i}$

$=\frac{3813}{100}$

$=38.13$

Now, sum of all current observations $=38.13\times 100=3813$

Required Mean =$39$

Therefore, required sum of all observations $=39\times 100=3900$

Therefore, extra matches that would be needed to be added to the total contents of the $100$ boxes to bring the mean to exactly $39=3900-3813=87$