Question

The prices of a movie ticket in 6 different movie theatres are Rs 50, Rs 80, Rs 120, Rs 200, Rs 100 and Rs 170. Find the standard deviation of the prices using the step-deviation method.

• A. 51.31
• B. 62.56
• C. 66.45
• D. 70.82

Answer 1

The correct option is A 51.31

Here, all observations are divisible by 10. Choose the common factor (c) as 10.

$Mean,\overline{X}=\frac{50+80+120+200+100+170}{6}=\frac{720}{6}=Rs120$

$Factoredmean,\overline{x}=\frac{120}{10}=12$

$\begin{array}{cccc}X& X^{\prime }=\frac{X}{c}& d=x-\overline{x}& d^2\\ 50& 5& -7& 49\\ 80& 8& -4& 16\\ 120& 12& 0& 0\\ 200& 20& 8& 64\\ 100& 10& -2& 4\\ 170& 17& 5& 25\\ & & & \sum d^2=158\end{array}$

$\sigma =\sqrt{\frac{\sum d^2}{N}}\times c=\sqrt{\frac{158}{6}}\times 10=5.131\times 10=51.31$