Question

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

$$\begin{array}{cc}Monthly& Number\\ savings\left(₹\right)& offamilies\\ 1000-2000& 14\\ 2000-3000& 15\\ 3000-4000& 21\\ 4000-5000& 27\\ 5000-6000& 25\end{array}$$

• A. ₹ 916.67
• B. ₹ 600.77
• C. ₹ 945.55
• D. ₹ 840

Answer 1

The correct option is D ₹ 840

Modal Class (class with highest frequency) is 4000 - 5000.

$\because Mode=l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h$
where $f_1$ represents the frequency of the modal class.
Also,
$l=$lower boundary of the modal class
$h=$ size of the modal class interval
$f_0=$ frequency of the class preceding the modal class
$f_2=$ frequency of the class succeeding the modal class

$\therefore \text{Here},f_1=27,f_0=21,f_2=25,I=4000,h=1000$

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

$=4750$

For finding mean, we use Direct method
(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.)

$Mean=\frac{\Sigma fx}{\Sigma f}$

$=3910$

$\therefore$ Difference between mode and mean is:
$=4750–3910=₹840$