Question

The distribution of weights of 50 students in a class is as follows.

$\begin{array}{ccccccc}Weight\left(kg\right)& 40-45& 45-50& 50-55& 55-60& 60-65& 65-70\\ No.ofstudents& 3& 7& 11& 12& 10& 7\end{array}$

Calculate the standard deviation using the step deviation method.

• A. 5.86
• B. 6.34
• C. 6.92
• D. 7.14

Answer 1

The correct option is D 7.14

Let the assumed mean be 52.5 i.e. A = 52.5 and the dividing factor (c) be 5.

$\begin{array}{cccccc}X& F& D& D^{\prime }=\frac{D}{c}& F{D}^{\prime }& F{D}^{\prime 2}\\ 42.5& 3& -10& -2& -6& 12\\ 47.5& 7& -5& -1& -7& 7\\ 52.5& 11& 0& 0& 0& 0\\ 57.5& 12& 5& 1& 12& 12\\ 62.5& 10& 10& 2& 20& 40\\ 67.5& 7& 15& 3& 21& 63\\ & \sum F=50& & & \sum F{D}^{\prime }=40& \sum F{D}^{\prime 2}=134\end{array}$

$\sigma =\sqrt{\frac{\sum F{D}^{\prime 2}}{\sum F}-{\left(\frac{\sum F{D}^{\prime }}{\sum F}\right)}^2}\times c=\sqrt{\frac{134}{50}-{\left(\frac{40}{50}\right)}^2}\times 5=\sqrt{2.68-0.64}\times 5=\sqrt{2.04}\times 5=1.428\times 5=7.14$