Question

The following data give the no of passengers travelling by Boeing 747 from one city to another in one week.

320, 290, 265, 300, 270, 315

Calculate the mean and standard deviation

Answer 1

Solution

Mean $\mu = \dfrac{\sum X_i}{N}$

Standard deviation $\sigma=\sqrt{\dfrac{\sum (X_i-\mu)^2}{N}}$

(a) Mean

$\mu =\frac{265+270+290+300+315+320}{6}$

$\mu =\dfrac{1760}{6}=293.33$

(b) Standard deviation

$\def\arraystretch{1.5}\begin{array}{c:c:c}X&X-\mu&(X-\mu)^2\\\hline265&-28.33&802.77\\\hdashline270&-23.33&544.44\\\hdashline290&-3.33&11.11\\\hdashline300&6.67&44.44\\\hdashline315&21.67&469.44\\\hdashline320&26.67&711.11\\\hline\sum &&2583.33\\\hline\end{array}$

$\sigma=\sqrt{\dfrac{2583.33}{6}}$

$\sigma=20.75$