Question

Find the Mean using Step deviation method if the following table :

$\begin{array}{ccccccccccc}\text{Marks}& \text{Below}10& \text{Below}20& \text{Below}30& \text{Below}40& \text{Below}50& \text{Below}60& \text{Below}70& \text{Below}80& \text{Below}90& \text{Below}100\\ \text{No. of students}& 5& 9& 17& 29& 45& 60& 70& 78& 83& 85\end{array}$

• A. 50.25
• B. 46.2
• C. 52
• D. 48.42

Answer 1

The correct option is D 48.42

$\begin{array}{cccccc}\text{Class Mark}& c_f& \text{Frequency(f)}& \text{Mid value(x)}& u=\frac{x-a}{c}& \text{fu}\\ 0-10& 5& 5& 5& -5& -25\\ 10-20& 9& 4& 15& -4& -16\\ 20-30& 17& 8& 25& -3& -24\\ 30-40& 29& 12& 35& -2& -24\\ 40-50& 45& 16& 45& -1& -16\\ 50-60& 60& 15& 55=A& 0& 0\\ 60-70& 70& 10& 65& 1& 10\\ 70-80& 78& 8& 75& 2& 16\\ 80-90& 83& 5& 85& 3& 15\\ 90-100& 85& 2& 95& 4& 8\\ \text{Total}& & \sum f=85& & & \sum fu=-56\end{array}$

Here a = 55 and h = 10

From cumulative frequencies given , we find the Frequencies of the class intervals.

Mean = a + $\frac{\sum fu}{\sum f}\times h$

= $55+\frac{-56}{85}\times 10$

= 55 + (-6.58)

= 55 - 6.58

= 48.42