Question

Find the mean and Mode of the following frequency distribution:

Class:	0-10	10-20	20-30	30-40	40-50	50-60	60-70
Frequencу:	8	7	15	20	12	8	10

Answer 1

1. The class midpoints are 5, 15, 25, 35, 45, 55 and 65.

The total frequency and weighted sum are:

\[\sum f_i=80,\quad \sum f_i x_i=8(5)+7(15)+15(25)+20(35)+12(45)+8(55)+10(65)=2850\]

2. Therefore, the mean is: \[\text{Mean}=\frac{2850}{80}=35.625\]

3. The modal class is 30 – 40. 

Here, l = 30, h = 10, f = 20, f₁ = 15 and f₂ = 12.

\[\text{Mode}=30+\frac{20-15}{2(20)-15-12}\times10=30+\frac{50}{13}\approx33.85\]

4. Therefore, the mean is 35.625 and the mode is approximately 33.85.