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The number of telephone calls received at an exchange per interval for 250 successive one-minute intervals are given in the following frequency table:
No. of calls ($x$): | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
No. of intervals ($f$): | 15 | 24 | 29 | 46 | 54 | 43 | 39 |
Given:
The number of telephone calls received at an exchange per interval for 250 successive one-minute intervals.
To do:
We have to compute the mean number of calls per interval.
Solution:
Let the assumed mean $A=4$
Number of calls ($x_i$) | Number of intervals ($f_i$) | $d_i=x_i -A$ ($A=4$) | $f_i \times\ d_i$ |
0 | 15 | $-4$ | $-60$ |
1 | 24 | $-3$ | $-72$ |
2 | 29 | $-2$ | $-58$ |
3 | 46 | $-1$ | $-46$ |
4 -$A$ | 54 | 0 | 0 |
5 | 43 | 1 | 43 |
6 | 39 | 2 | 78 |
Total | $\sum{f_i}=250$ | $\sum{f_id_i}=-115$ |
Mean $=A+\frac{\sum{f_id_i}}{\sum{f_i}}$
Therefore,
Mean $=4+\frac{-115}{250}$
$=4+\frac{-23}{50}$
$=\frac{4(50)-23}{50}$
$=\frac{177}{50}$
$=3.54$
The mean number of calls per interval is $3.54$.
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