Question

Find the mean of the step deviations:
$\begin{array}{ccccc}Classinterval& Frequency\left(f_i\right)& Classmark\left(x_i\right)& d_i=x_i-a& u_i=\frac{d_i}{h}\\ 0-100& 40& 50& -200& -2\\ 100-200& 39& 150& -100& -1\\ 200-300& 34& 250& 0& 0\\ 300-400& 30& 350& 100& 1\\ 400-500& 45& 450& 200& 2\end{array}$

• A. $0$
• B. $\frac{1}{188}$
• C. $250$
• D. $250.52$

Answer 1

The correct option is B

$\frac{1}{188}$

$$\begin{array}{cccccc}Classinterval& Frequency\left(f_i\right)& Classmark\left(x_i\right)& d_i=x_i-a& u_i=\frac{d_i}{h}& f_i{u}_i\\ 0-100& 40& 50& -200& -2& -80\\ 100-200& 39& 150& -100& -1& -39\\ 200-300& 34& 250& 0& 0& 0\\ 300-400& 30& 350& 100& 1& 30\\ 400-500& 45& 450& 200& 2& 90\\ Total& \sum f_i=188& & & & \sum f_i{u}_i=1\end{array}$$

Mean of step deviations $=a+h\left(\frac{\sum f_i{u}_i}{\sum f_i}\right)$

Where h = Difference between upper limit and lower limit

a = Assumed mean

$=250+100\times \frac{1}{188}$

= 250.53

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