Question

An aircraft has 120 passenger seats. The number of seats occupied during 100 flights is given in the following table.
$\begin{array}{cccccc}\text{Number of seats}& 100-104& 104-108& 108-112& 112-116& 116-120\\ \text{Frequency}& 15& 20& 32& 18& 15\end{array}$
Determine the mean number of seats occupied over the flights.

Answer 1

We first, find the class mark $x_i$ of each class and then proceed as follows.
$\begin{array}{ccccc}\text{Number of seats \& Class marks}\left(x_i\right)& \text{Frequency}\left(f_i\right)& \text{Deviation}{d}_i=x_i-a& f_i{d}_i& \\ 100-104& 102& 15& -8& -120\\ 104-108& 106& 20& -4& -80\\ 108-112& a=110& 32& 0& 0\\ 112-116& 114& 18& 4& 72\\ 116-120& 118& 15& 8& 120\\ & & N=\sum f_i=100& & \sum f_i{d}_i=-8\end{array}\therefore Assumedmean,a=110,$
Class width, h = 4
and total observation, N = 100
By assumed mean method,
$Mean\left(\overline{x}\right)=a+\frac{\sum f_i{d}_i}{\sum f_i}=110+\left(\frac{-8}{100}\right)=110-0.08=109.92$