Selina Concise Class 10 Math Chapter 24 Exercise 24B Measures of Central Tendency Solutions
Exercise – 24B
(Q1) 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 class interval (C.I) | Class Mark (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 |
Σfi = 50 | Σfixi = 1074 |
Class Mark (xi) = 16+18/2 = 17
18+20/2 = 19
20+22/2 = 21
22+24/2 = 23
24+26/2 = 25
Now, we have to find mean,
Mean Σfixi/Σfi
= 1074/50
Mean = 21.48
(Q2) The following table gives the weekly wages of workers in a factory.
Weekly wages (RS) | 50 – 55 | 55 – 60 | 60 – 65 | 65 – 70 | 70 – 75 | 75 – 80 |
Number of workers | 5 | 20 | 10 | 10 | 9 | 6 |
80 – 85 | 85 – 90 |
12 | 8 |
Calculate the mean by using:
(i) Direct method
(ii) Short – cut method
Solution:
(i) Direct method
Weekly wages (RS) | Class Mark (xi) | Number 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 | 652.0 |
75 – 80 | 77.5 | 6 | 465.0 |
80 – 85 | 82.5 | 12 | 990.0 |
85 – 90 | 87.5 | 8 | 700.0 |
Σxi = 80 | Σfixi = 5520.00 |
Class mark (xi) =
(i) 50+55/2 = 52.5
(ii) 55+60/2 = 57.5
(iii) 60+65/2 = 62.5
(iv) 65+70/2 = 67.5
(v) 70+75/2 = 72.5
(vi) 75+80/2 = 77.5
(vii) 80+85/2 = 82.5
(viii) 85+90/2 = 87.5
Now, we have to find mean –
Mean = Σ fixi/ Σxi
= 5520/80
Mean = 69
(ii) Short – cut method
Weekly wages (RS) | Number of workers (fi) | Class mark (xi) | A = 72.5
di = x -A |
Fidi |
50 – 55 | 5 | 52.5 | -20 | -100 |
55 – 60 | 20 | 87.5 | -15 | -300 |
60 – 65 | 10 | 62.5 | -10 | -100 |
65 – 70 | 10 | 67.5 | -5 | -50 |
70 – 75 | 9 | 72.5 – A | 0 | 0 |
75 – 80 | 6 | 77.5 | 5 | 30 |
80 – 85 | 12 | 82.5 | 10 | 120 |
85 – 90 | 8 | 87.5 | 15 | 120 |
Total | Σfi = 80 | Σfidi = -280 |
A = 72.5
Class Mark (xi) = (i) 50+55/2 = 52.5
(ii) 55+60/2 = 57.5
(iii) 60+65/2 = 62.56
(iv) 65+70/2 = 67.5
(v) 70+75/2 = 72.5
(vi) 75+80/2 = 77.5
(vii) 80+85/2 = 82.5
(viii) 85+90/2 = 87.5
Now, x̄ = A + Σfidi/Σfi
= 72.5 + (-280/80)
= 72.5 – 3.5
x̄ = 69
Here is your solution of Selina Concise Class 10 Math Chapter 24 Exercise 24B Measures of Central Tendency
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