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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

Solution:

Given, the data represents the frequency and cumulative frequency of heights of students in a class.

We have to find the values of the unknown entries a, b, c, d, e, f.

Height in cm	Frequency	Cumulative frequency	Cumulative frequency calculation
150 - 155	12	a	a = 12
155 - 160	b	25	a + b = 12 + b
160 - 165	10	c	12 + b + 10 = 22 + b
165 - 170	d	43	22 + b + d
170 - 175	e	48	22 + b + d + e
175 - 180	2	f	22 + b + d + e + 2

From the table,

12 + b = 25

b = 25 - 12

b = 13

22 + b = c

c = 22 + 13

c = 35

22 + b + d = 43

22 + 13 + d = 43

35 + d = 43

d = 43 - 35

d = 8

22 + b + d + e = 48

22 + 13 + 8 + e = 48

35 + 8 + e = 48

43 + e = 48

e = 48 - 43

e = 5

22 + b + d + e + 2 = f

22 + 13 + 8 + 5 + 2 = f

f = 50

Therefore, the values of unknown entries are a = 12, b = 13, c = 35, d = 8, e = 5, f = 50.

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

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 14

NCERT Exemplar Class 10 Maths Exercise 13.3 Problem 12

Summary:

The unknown entries in the distribution of heights of students in a class are a = 12, b = 13, c = 35, d = 8, e = 5, f = 50

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