Question

Find the mode of the following distribution:

Weight (in kgs)	25 − 34	35 − 44	45 − 54	55 − 64	65 − 74	75 − 84
Number of students	4	8	10	14	8	6

Answer 1

In the given table the class intervals are in inclusive form; convert them into exclusive form.

Class	Mid value (x)	frequency (f)	fx	cf
24.5 − 34.5	29.5	4	118	4
34.5 − 44.5	39.5	8	316	12
44.5 − 54.5	49.5	10	495	22
54.5 − 64.5	59.5	14	833	36
64.5 − 74.5	69.5	8	556	44
74.5 − 84.5	79.5	6	477	50
		`sumf` = 50	`sumfx` = 2975

The highest frequency is 14

Modal class is 54.5 – 64.5

Here l = 54.5, f = 14, f₁ = 10, f₂ = 8 and c = 10

mode = `"l" + ((f - f_1)/(2f - f_1 - f_2)) xx "c"`

= `54.5 + ((14 - 10))/((28 - 10 - 8)) xx 10`

= `54.5 + (4 xx 10)/10`

= 58.5

∴ Mode = 58.5