The given distribution shows the runs scored by batsmen in one-day cricket matches.
We are asked to find the mean number of runs.
| Runs scored |
0-40 |
40-80 |
80-120 |
120-160 |
160-200 |
| Number of batsmen |
12 |
20 |
35 |
30 |
23 |
Let us create the cumulative frequency table for the given data.
| Runs scored |
Number of batsmen (fi) |
Class mark(xi) |
(fixi) |
| 0-40 |
12 |
20 |
12 × 20 = 240 |
| 40-80 |
20 |
60 |
20 × 60 = 1200 |
| 80-120 |
35 |
100 |
35 × 100 = 3500 |
| 120-160 |
30 |
140 |
30 × 140 = 4200 |
| 160-200 |
23 |
180 |
23 × 180 = 4140 |
|
∑fi = 120 |
|
∑fixi = 240 + 1200 + 3500 + 4200 + 4140 = 13280 |
The mean \(\bar x = \frac{\sum f_i x_i}{\sum f_i}\)
\(= \frac{13280}{120}\)
\(= 110.67\)
