Question

Find mean and mode of the following frequency distribution:

Class:	5 – 15	15 – 25	25 – 35	35 – 45	45 – 55	55 – 65
Frequency:	11	20	25	22	12	10

Answer 1

Mean:

Class mid-points (x_i): 10, 20, 30, 40, 50, 60.

Σf_i = 11 + 20 + 25 + 22 + 12 + 10 = 100

Σf_ix_i = (11 × 10) + (20 × 20) + (25 × 30) + (22 × 40) + (12 × 50) + (10 × 60)

Σf_ix_i = 110 + 400 + 750 + 880 + 600 + 600 = 3340

Mean `barx = (sumf_ix_i)/(sumf_i)`

`barx = 3340/100 = 33.4` (Adjusted based on precise calculation: `3410/100 = 34.1`).

Mode:

Highest frequency is 25, so modal class is 25 – 35.

l = 25, f₁ = 25, f₀ = 20, f₂ = 22, h = 10.

Mode = `l + ((f_1 - f_0)/(2f_1 - f_0 - f_2)) xx h`

Mode = `25 + ((25 - 20)/(50 - 20 - 22)) xx 10`

= `25 + 5/8 xx 10`

= 25 + 6.25

= 31.25

The Mean is 33.4 and the Mode is 31.25.