Question

The following table gives the daily income of 50 cab drivers of a particular city

Income (₹)	500 - 600	600 - 700	700 - 800	800 - 900	900 - 1000
No. of Drivers	12	14	8	6	10

Find the mean income and the modal income.

Answer 1

1. The class midpoints are ₹ 550, ₹ 650, ₹ 750, ₹ 850 and ₹ 950.

The total frequency and weighted sum are:

\[\sum f_i=50,\quad \sum f_i x_i=12(550)+14(650)+8(750)+6(850)+10(950)=36300\]

2. Therefore, the mean income is:

\[\text{Mean}=\frac{36300}{50}=₹726\]

3. The modal class is ₹ 600 – ₹ 700. 

Here, l = 600, h = 100, f = 14, f₁ = 12 and f₂ = 8.

\[\text{Mode}=600+\frac{14-12}{2(14)-12-8}\times100=₹625\]

4. Therefore, the mean income is ₹ 726 and the modal income is ₹ 625.