Question

Find the unknown entries a, b, c, d, e, f in the following distribution of heights of students in a class:

Height (in cm)	Frequency	Cumulative frequency
150 – 155	12	a
155 – 160	b	25
160 – 165	10	c
165 – 170	d	43
170 – 175	e	48
175 – 180	2	f
Total	50

Answer 1

Height (in cm)	Frequency	Cumulative frequency (given)	Cumulative frequency
150 – 155	12	a	12
155 – 160	b	25	12 + b
160 – 165	10	c	22 + b
165 – 170	d	43	22 + b + d
170 – 175	e	48	22 + b + d + e
175 – 180	2	f	24 + b + d + e
Total	50

On comparing last two tables, we get

a = 12

∴ 12 + b = 25

⇒ b = 25 – 12 = 13

22 + b = c

⇒ c = 22 + 13 = 35

22 + b + d = 43

⇒ 22 + 13 + d = 43

⇒ d = 43 – 35 = 8

And 22 + b + d + e = 48

⇒ 22 + 13 + 8 + e = 48

⇒ e = 48 – 43 = 5

And 24 + b + d + e = f

⇒ 24 + 13 + 8 + 5 = f

∴ f = 50