# An aircraft has 120 passenger seats. The number of seats occupied during 100 flights is given in the following table : no.of seats 100-104 104-108 108-112 112-116 116-120 Frequency 15 20 32 18 15 Determine the mean number of seats occupied over the flights.

Solution.  Here we calculate mean by following the given steps:

1. Find the mid point of each interval.
2. Multiply the frequency of each interval by its mid point.
3. Get the sum of all the frequencies (f) and sum of all the (fx)
4. Now divide sum of (fx) by sum of (f)
 Number of seats Frequency fi xi fixi 100-104 15 102 1530 104-108 20 106 2120 108-112 32 110 3520 112-116 18 114 2052 116-120 15 118 177065268 $\sum f_{i}= 100$ $\sum f_{i}x_{i}= 10992$

$mean\left ( \bar{x} \right )= \frac{\sum f_{i}x_{i}}{\sum f_{i}}= \frac{10992}{100}= 109\cdot 92$
number of seats = 109

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