Find the mean (correct to one place of decimal ) by using short-cut method . x 40 41 43 45 46 49 50 f 14 28 38 50 40 20 10

Assume mean = 45 = A x f d = x - A fd 40 14 - 5 - 70 41 28 - 4 - 112 43 38 - 2 - 76 45 50 0 0 46 40 1 40 49 20 4 80 50 10 5 50 total 200 - 88 Mean = A + Σ f d Σ f = 45 + - 88 200 = 1125 - 11 25 = 44 . 6

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 Number of students. 2 7 21 17 3

age x i Number of students f i x i f i 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 x - = Σ f i x i Σ f i = 1074 50 = 21 . 48

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 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 No. of workers 5 20 10 10 9 6 12 8 Calculate the mean, by using: Short-Cut method

Weekly wages Number of workers ( f i ) mid-point ( x i ) d = x - A f i d i 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 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 x = A + Σ f i x i Σ f i = 72 . 5 + - 280 80 x = 72 . 5 - 3 . 5 x = 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 Number of boys 10 12 14 12 9 7 6 Calculate the mean by Short -cut method

Marks No.of boys ( f i ) Mid-value ( x i ) a = 65 d = x i - A f i d i 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 x = A + ∑ f i d i ∑ f i = 65 + - 270 70 = 61 . 14

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

Find mean by 'step-deviation method': C.I. 63 - 70 70 - 77 77 - 84 84 - 91 91 - 98 98 - 105 105 - 112 Frequency 9 13 27 38 32 16 15

C . I . frequency ( f i ) Mid-value xi A = 87 . 5 d = x i - A h f i d i 63 - 70 9 66 . 5 - 3 - 27 70 - 77 13 73 . 5 - 2 - 26 77 - 84 27 80 . 5 - 1 - 27 84 - 91 38 87 . 5 0 0 91 - 98 32 94 . 5 1 32 98 - 105 16 101 . 5 2 32 105 - 112 15 108 . 5 3 45 Total 150 29 A = 87 . 50 and h = 7 x = A + h ∑ f i d i ∑ f i = 87 . 5 + 7 + × 29 150 x = 88 . 85

MEDIUM

10th ICSE

IMPORTANT

Earn 100

In the following table, $\underset{}{\sum f_{i} = 200}$ and mean $= 73 .$ Find the missing frequencies $f_{1,}$ and $f_{2}$ .

$x_{i}$ $0$ $50$ $100$ $150$ $200$ $250$

$f_{i}$ $46$ $f_{1}$ $f_{2}$ $25$ $10$ $5$

Important Questions on Measures of Central Tendency (Mean, Median, Quartiles and Mode)

MEDIUM

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 14

Find the arithmetic mean ( correct to the nearest whole-number) by using step-deviation method.

$x$	$5$	$10$	$15$	$20$	$25$	$30$	$35$	$40$	$45$	$50$
$y$	$f_{2} = 38$	$43$	$75$	$67$	$72$	$45$	$39$	$9$	$8$	$6$

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 15

Find the mean (correct to one place of decimal ) by using short-cut method .

$x$	$40$	$41$	$43$	$45$	$46$	$49$	$50$
$f$	$14$	$28$	$38$	$50$	$40$	$20$	$10$

MEDIUM

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 1

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

Age (years)	$16 - 18$	$18 - 20$	$20 - 22$	$22 - 24$	$24 - 26$
Number of students.	$2$	$7$	$21$	$17$	$3$

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 2

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

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

Calculate the mean, by using:

Short-Cut 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	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$	$90 - 100$
Number of boys	$10$	$12$	$14$	$12$	$9$	$7$	$6$

Calculate the mean by Short -cut 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 4

Find mean by 'step-deviation method':

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

$x_{i}$	$0$	$50$	$100$	$150$	$200$	$250$
$f_{i}$	$46$	$f_{1}$	$f_{2}$	$25$	$10$	$5$

In the following table,∑fi=200 and mean =73. Find the missing frequencies f1, and f2. xi 0 50 100 150 200 250 fi 46 f1 f2 25 10 5

Important Questions on Measures of Central Tendency (Mean, Median, Quartiles and Mode)

Learn and Prepare for any exam you want !

In the following table, $\underset{}{\sum f_{i} = 200}$ and mean $= 73 .$ Find the missing frequencies $f_{1,}$ and $f_{2}$ .

$x_{i}$ $0$ $50$ $100$ $150$ $200$ $250$

$f_{i}$ $46$ $f_{1}$ $f_{2}$ $25$ $10$ $5$