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 80 - 85 85 - 90 Number of workers 5 20 10 10 9 6 12 8 Calculate the mean,by using direct Method.

Weekly wages mid-value ( x i ) Number of workers ( f i ) f i x i 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 total 80 5520 . 00 x - = Σ f i x i Σ f i = 5520 80 = 69

The following are the marks obtained by 70 boys in a class test. Marks 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 90 - 100 No. of boys. 10 12 14 12 9 7 6 Calculate the mean by: Step-deviation Method.

step- deviation method. Marks Number of boys ( f i ) mid-value ( x i ) A = 65 u = x i - A h f i u i 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 A = 65 and h = 10 x = A + h x i ∑ f i u i ∑ f i = 65 + 10 × - 27 70 x = 61 . 14

The mean of following frequency distribution is 21 1 7 . Find the value of ' f ' . Class interval 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 Frequency 8 22 31 f 2

x = 21 1 7 = 148 7 C . I . Frequency ( f i ) Mid-value ( x i ) f i x i 0 - 10 8 5 40 10 - 20 22 15 330 20 - 30 31 25 775 30 - 40 f 35 35 f 40 - 50 2 45 90 Total 63 + f 1235 + 35 f x = ∑ f i x i ∑ f i = 1235 + 35 f 63 + f = 148 7 = 1235 + 35 f 63 + f 245 f - 148 f = 9324 - 8645 f = 679 97 f = 7

Using step-division method,calculate the mean marks of the following distribution. Class interval 50 - 55 55 - 60 60 - 65 65 - 70 70 - 75 75 - 80 80 - 85 85 - 90 Frequency 5 20 10 10 9 6 12 8

C . I . f i Midvalue ( x i ) d i = x i - A f i d i 50 - 55 5 52 . 5 - 20 - 100 55 - 60 20 51 . 5 - 15 - 300 60 - 65 10 62 . 5 - 10 - 100 65 - 70 10 67 . 5 - 5 - 50 70 - 75 9 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 Mean = A + ∑ f i d i ∑ f i = 72 . 5 + - 280 80 = 69

If the mean of the following observations is 54 , find the value of p . Class: 0 - 20 20 - 40 40 - 60 60 - 80 80 - 100 Frequency: 7 p 10 9 13

Class Frequency ( f ) Midvalue ( x ) fx 0 - 20 7 10 70 20 - 40 P 30 30 P 40 - 60 10 50 500 60 - 80 9 70 630 80 - 100 13 90 1170 Total 39 + P 2370 + 30 P x = ∑ f x ∑ f = 2370 + 30 P 39 + P . . . . ( i ) mean = 54 . . . ( ii ) from ( i ) and ( ii ) 2370 + 30 P 39 + P = 54 P = 11

Calculate the mean of the distribution, given below, using the shortcut method: Marks 11 - 20 21 - 30 31 - 40 41 - 50 51 - 60 61 - 70 71 - 80 Number of students 2 6 10 12 9 7 4

Marks f x d = x - A A = 45 . 5 fd 11 - 20 2 15 . 5 - 30 - 60 21 - 30 6 25 . 5 - 20 - 120 31 - 40 10 35 . 5 - 10 - 100 41 - 50 12 45 . 5 0 0 51 - 60 9 55 . 5 10 90 61 - 70 7 65 . 5 20 140 71 - 80 4 75 . 5 30 120 Total 50 70 Mean = A + ∑ f d ∑ f = 45 . 5 + 70 50 Mean = 46 . 9

R K Bansal Solutions for Exercise 1: EXERCISE

Author:R K Bansal

R K Bansal Mathematics Solutions for Exercise - R K Bansal Solutions for Exercise 1: EXERCISE

Attempt the practice questions from Exercise 1: EXERCISE with hints and solutions to strengthen your understanding. Concise Mathematics solutions are prepared by Experienced Embibe Experts.

Questions from R K Bansal Solutions for Exercise 1: EXERCISE with Hints & Solutions

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 2

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

Weekly Wages (Rs)	$50 - 55$	$55 - 60$	$60 - 65$	$65 - 70$	$70 - 75$	$75 - 80$	$80 - 85$	$85 - 90$
Number of workers	$5$	$20$	$10$	$10$	$9$	$6$	$12$	$8$

Calculate the mean,by using direct Method.

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 3

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

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

Calculate the mean by: Step-deviation Method.

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 5

The mean of following frequency distribution is $21 \frac{1}{7}$ . Find the value of ' $f$ ' .

Class interval	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
Frequency	$8$	$22$	$31$	$f$	$2$

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 6

Using step-division method,calculate the mean marks of the following distribution.

Class interval	$50 - 55$	$55 - 60$	$60 - 65$	$65 - 70$	$70 - 75$	$75 - 80$	$80 - 85$	$85 - 90$
Frequency	$5$	$20$	$10$	$10$	$9$	$6$	$12$	$8$

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 7

Using the information given in the adjoining histrogram;calculate the mean.

Question Image

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 8

If the mean of the following observations is $54$ , find the value of $p$ .

Class:	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$
Frequency:	$7$	$p$	$10$	$9$	$13$

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 9

The mean of the following distribution is $62.8$ and the sum of all the frequencies is $50 .$ Find the missing frequencies $f_{1}$ and $f_{2}$

Class:	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$	$100 - 120$
Frequency :	$5$	$f_{1}$	$10$	$f_{2}$	$7$	$8$

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 10

Calculate the mean of the distribution, given below, using the shortcut method:

Marks	$11 - 20$	$21 - 30$	$31 - 40$	$41 - 50$	$51 - 60$	$61 - 70$	$71 - 80$
Number of students	$2$	$6$	$10$	$12$	$9$	$7$	$4$

R K Bansal Solutions for Exercise 1: EXERCISE

R K Bansal Mathematics Solutions for Exercise - R K Bansal Solutions for Exercise 1: EXERCISE

Questions from R K Bansal Solutions for Exercise 1: EXERCISE with Hints & Solutions

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