Selina Solutions Concise Maths Class 10 Chapter 24 Measures of Central Tendency Exercise 24(B)

Selina Solutions Class 10 Maths Chapter 24 Measures of Central Tendency

Recalling the concepts learned from the previous chapter, the practice consists of a mixture of problems based on extracting the mean, median, polymer, and pylon for appropriate questions. If students are looking for a resource to clarify their doubts, stop here at Selina Solutions of Class 10 Mathematics as these solutions have been created by experts from Mathematics PDF Solutions keeping in mind the latest ICSE patterns. These practice solutions are short Selina solutions for class 10 mathematics chapter 24 central trend practice measures pdf available in the following link.

Exercise 24(A) Solutions

Exercise 24(B) Solutions

Exercise 24(C) Solutions

Exercise 24(D) Solutions

Exercise 24(E) Solutions

Selina Solutions Concise Maths Class 10 Chapter 24 Measures of Central Tendency Exercise 24(B)

1. The following table gives the ages of 50 students of a class. Find the arithmetic mean of their ages.

Age – Years	16 – 18	18 – 20	20 – 22	22- 24	24-26
No. of Students	2	7	21	17	3

Solution:

Age in years C.I.	xi	Number of students (fi)	xifi
16 – 18	17	2	34
18 – 20	19	7	133
20 – 22	21	21	441
22 – 24	23	17	391
24 – 26	25	3	75
Total		50	1074

Mean = ∑fi xi/ ∑fi = 1074/50 = 21.48

2. The following table gives the weekly wages of workers in a factory.

Weekly Wages (Rs)	No. of Workers
50-55	5
55-60	20
60-65	10
65-70	10
70-75	9
75-80	6
80-85	12
85-90	8

Calculate the mean by using:

(i) Direct Method

(ii) Short – Cut Method

Solution:

(i) Direct Method

Weekly Wages (Rs)	Mid-Value xi	No. of Workers (fi)	fixi
50-55	52.5	5	262.5
55-60	57.5	20	1150.0
60-65	62.5	10	625.0
65-70	67.5	10	675.0
70-75	72.5	9	652.5
75-80	77.5	6	465.0
80-85	82.5	12	990.0
85-90	87.5	8	700.0
Total		80	5520.00

Mean = ∑fi xi/ ∑fi = 5520/80 = 69

(ii) Short – cut method

Weekly wages (Rs)	No. of workers (fi)	Mid-value xi	A = 72.5 di = x – A	fidi
50-55	5	52.5	-20	-100
55-60	20	57.5	-15	-300
60-65	10	62.5	-10	-100
65-70	10	67.5	-5	-50
70-75	9	A = 72.5	0	0
75-80	6	77.5	5	30
80-85	12	82.5	10	120
85-90	8	87.5	15	120
Total	80			-280

Here, A = 72.5

Selina Solutions Concise Class 10 Maths Chapter 24 ex. 24(B) - 1

3. The following are the marks obtained by 70 boys in a class test:

Marks	No. of boys
30 – 40	10
40 – 50	12
50 – 60	14
60 – 70	12
70 – 80	9
80 – 90	7
90 – 100	6

Calculate the mean by:

(i) Short – cut method

(ii) Step – deviation method

Solution:

(i) Short – cut method

Marks	No. of boys (fi)	Mid-value xi	A = 65 di = x – A	fidi
30 – 40	10	35	-30	-300
40 – 50	12	45	-20	-240
50 – 60	14	55	-10	-140
60 – 70	12	A = 65	0	0
70 – 80	9	75	10	90
80 – 90	7	85	20	140
90 – 100	6	95	30	180
Total	70			-270

Here, A = 65

Selina Solutions Concise Class 10 Maths Chapter 24 ex. 24(B) - 2

(ii) Step – deviation method

Marks	No. of boys (fi)	Mid-value xi	A = 65 ui = (xi – A)/ h	fiui
30 – 40	10	35	-3	-30
40 – 50	12	45	-2	-24
50 – 60	14	55	-1	-14
60 – 70	12	A = 65	0	0
70 – 80	9	75	1	9
80 – 90	7	85	2	14
90 – 100	6	95	3	18
Total	70			-27

Here, A = 65 and h = 10

Selina Solutions Concise Class 10 Maths Chapter 24 ex. 24(B) - 3

4. Find mean by step – deviation method:

C. I.	63-70	70-77	77-84	84-91	91-98	98-105	105-112
Freq	9	13	27	38	32	16	15

Solution:

C. I.	Frequency (fi)	Mid-value xi	A = 87.50 ui = (xi – A)/ h	fiui
63 – 70	9	66.50	-3	-27
70 – 77	13	73.50	-2	-26
77 – 84	27	80.50	-1	-27
84 – 91	38	A = 87.50	0	0
91 – 98	32	94.50	1	32
98 – 105	16	101.50	2	32
105 – 112	15	108.50	3	45
Total	150			29