Question

Find the Mean and Mode of the following data:

Class:	4-8	8-12	12-16	16-20	20-24	24-28	28-32	32-36
Frequency:	2	12	15	25	18	12	13	3

Answer 1

1. The class midpoints are 6, 10, 14, 18, 22, 26, 30 and 34.

The total frequency is 100 and:

\[\sum f_i x_i=2(6)+12(10)+15(14)+25(18)+18(22)+12(26)+13(30)+3(34)=1992\]

2. Therefore, the mean is: \[\text{Mean}=\frac{1992}{100}=19.92\]

3. The modal class is 16 – 20, with frequency 25. 

Here, l = 16, h = 4, f₁ = 15 and f₂ = 18.

\[\text{Mode}=16+\frac{25-15}{2(25)-15-18}\times4=16+\frac{40}{17}\approx18.35\]

4. Therefore, the mean is 19.92 and the mode is approximately 18.35.