Question

The following data shows monthly savings of 100 families . Find the difference of modal and mean monthly savings lies between.

$$\begin{array}{cc}\text{Monthly savings(Rs)}& \text{Number families}\\ 1000-2000& 14\\ 2000-3000& 15\\ 3000-4000& 21\\ 4000-5000& 27\\ 5000-6000& 25\end{array}$$

• A. 700-800
• B. 600-700
• C. 900-1000
• D. 800 - 900

Answer 1

The correct option is C

900-1000

Modal class is 4000-5000 with

$f_1$ = 27, $f_0$ = 21, $f_2$ = 25, I = 4000, h = 1000

Mode = l + $\frac{f_1-f_0}{{2f}_1-f_0-f_2}\times h$

For finding mean , we use Direct method

Mode = 4000 + $\frac{6}{8}$$\times$1000

= 4750

Mean = 3833.33

We used Direct method to find the mean because the numbers are very easy even though they are large. You could use any of the three methods.

Difference between mode and mean = 4750 – 3833.33 = 916.67.