Find the median from the given frequency distribution. Class Interval 70 - 74 75 - 79 80 - 84 85 - 89 90 - 94 95 - 99 105 - 109 110 - 114 115 - 119 Frequency 15 25 30 4 10 8 6 4 3

Given data is Class Interval 70 - 74 75 - 79 80 - 84 85 - 89 90 - 94 95 - 99 105 - 109 110 - 114 115 - 119 Frequency 15 25 30 4 10 8 6 4 3 Now, let prepare the cumulative frequency distribution table for the given data, Class Interval Frequency Cumulative frequency 69 . 5 - 74 . 5 15 15 74 . 5 - 79 . 5 25 15 + 25 = 40 79 . 5 - 84 . 5 30 40 + 30 = 70 84 . 5 - 89 . 5 4 70 + 4 = 74 89 . 5 - 94 . 5 10 10 + 74 = 84 94 . 5 - 99 . 5 8 84 + 8 = 93 99 . 5 - 105 . 5 6 93 + 6 = 99 105 . 5 - 109 . 5 4 99 + 4 = 103 109 . 5 - 114 . 5 3 103 + 3 = 106 N = ∑ f = 106 N 2 = 106 2 = 53 ∴ Median = l + N 2 - F f m × i , where l is the boundary of the median class, F is the cumulative frequency of the class preceding the median class, f m is the frequency of the median class, i is the length of the median class, N = Total frequency Here, l = 79 . 5 , F = 40 , f m = 30 , i = 79 . 5 - 84 . 5 = 5 , N = 106 On substituting the values, we get, Median = 79 . 5 + 53 - 40 30 × 5 = 79 . 5 + 13 6 = 81 . 6 Hence, the median for the given data is 81 . 6 .

From the given data, find the median of the height of the students of a class. Height cm 161 - 167 167 - 173 173 - 179 179 - 185 185 - 191 191 - 197 Number of students 79 92 60 22 5 3

Given data is Height cm 161 - 167 167 - 173 173 - 179 179 - 185 185 - 191 191 - 197 Number of students 79 92 60 22 5 3 Now, let us prepare the frequency distribution table for the given data. Height cm Number of students f Cumulative frequency 161 - 167 79 79 167 - 173 ( Median class ) 92 79 + 92 = 171 173 - 179 60 171 + 60 = 231 179 - 185 22 231 + 22 = 253 185 - 191 5 253 + 5 = 258 191 - 197 3 258 + 3 = 261 N = ∑ f = 261 N 2 = 261 2 = 130 . 5 ∴ Median = l + N 2 - F f m × i , where l is the boundary of the median class, F is the cumulative frequency of the class preceding the median class, f m is the frequency of the median class, i is the length of the median class, N = Total frequency Here, l = 167 , F = 79 , f m = 92 , i = 173 - 167 = 6 , N 2 = 130 . 5 On substituting the values, we get, Median = 167 + 130 . 5 - 79 92 × 6 = 167 + 51 . 5 92 × 6 = 167 + 3 . 36 = 170 . 36 Hence, the median for the given data is 170 . 36 , approximately.

From the given data, if the median is 46 , then find x and y when the sum of frequencies is 230 . Class boundary 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 Frequency 12 30 x 65 y 25 18

Given data is Class boundary 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 Frequency 12 30 x 65 y 25 18 Now, let us prepare the frequency distribution table for the given data. Class boundary Frequency f Cumulative frequency 10 - 20 12 12 20 - 30 30 12 + 30 = 42 30 - 40 x 42 + x 40 - 50 ( Median class ) 65 42 + x + 65 = 107 + x 50 - 60 y 107 + x + y 60 - 70 25 132 + x + y 70 - 80 18 18 + 132 + x + y = 150 + x + y N = 150 + x + y N 2 = 150 + x + y 2 ∴ Median = l + N 2 - F f m × i , where l is the boundary of the median class, F is the cumulative frequency of the class preceding the median class, f m is the frequency of the median class, i is the length of the median class, N = Total frequency Here, l = 40 , F = 42 + x , f m = 65 , i = 50 - 40 = 10 , N 2 = 150 + x + y 2 On substituting the values, we get, Median = 40 + 150 + x + y 2 - 42 + x 65 × 10 ⇒ 46 = 40 + 150 + x + y - 84 - 2 x 130 × 10 ⇒ 46 = 40 + 66 - x + y 13 ⇒ 78 = 66 - x + y ⇒ - x + y = 78 - 66 = 12 ⇒ y - x = 12 . . . . . . . . . . . . . . i Given that the sum of frequencies is 230 . ⇒ N = x + y + 150 = 230 ⇒ x + y = 230 - 150 = 80 . . . . . . . . . . . . . . . . ii Adding equations i and ii , we get, 2 y = 92 ⇒ y = 92 2 = 46 Substituting the value of y in equation i , we get, 46 - x = 12 ⇒ - x = 12 - 46 = - 34 ⇒ x = 34 Hence, x = 34 and y = 46 .

HARD

10th West Bengal Board

IMPORTANT

Earn 100

Find the median from the given data.

Income $(₹)$ $100$ $150$ $80$ $200$ $250$ $180$

Number of persons $24$ $26$ $16$ $20$ $6$ $30$

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Important Questions on Measures of Central Tendency

HARD

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 9 - Measures of Central Tendency>EXERCISE 1B>Q 6

Find the median from the given frequency distribution.

Marks obtained	$0 - 10$	$10 - 30$	$30 - 60$	$60 - 70$	$70 - 90$
Number of female students	$15$	$25$	$30$	$4$	$10$

HARD

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 9 - Measures of Central Tendency>EXERCISE 1B>Q 7

Find the median from the given frequency distribution.

Class Interval	$70 - 74$	$75 - 79$	$80 - 84$	$85 - 89$	$90 - 94$	$95 - 99$	$105 - 109$	$110 - 114$	$115 - 119$
Frequency	$15$	$25$	$30$	$4$	$10$	$8$	$6$	$4$	$3$

HARD

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 9 - Measures of Central Tendency>EXERCISE 1B>Q 8

Find the median from the given data.

Mid-value	$15$	$25$	$35$	$45$	$55$	$65$	$75$	$85$	$95$
Frequency	$6$	$8$	$10$	$2$	$4$	$7$	$9$	$4$	$6$

HARD

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 9 - Measures of Central Tendency>EXERCISE 1B>Q 9

From the given data, find the median of the height of the students of a class.

Height $(cm)$	$161 - 167$	$167 - 173$	$173 - 179$	$179 - 185$	$185 - 191$	$191 - 197$
Number of students	$79$	$92$	$60$	$22$	$5$	$3$

HARD

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 9 - Measures of Central Tendency>EXERCISE 1B>Q 10

An incomplete frequency distribution table is given. If from the complete distribution the median obtained is $53.1 kg$ , then find the missing frequency $x$ .

Weight $(kg)$	$46 - 48$	$49 - 51$	$52 - 54$	$55 - 57$	$58 - 60$
Number of girls	$5$	$8$	$15$	$x$	$4$

HARD

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 9 - Measures of Central Tendency>EXERCISE 1B>Q 11

From the given data, if the median is $46$ , then find $x$ and $y$ when the sum of frequencies is $230$ .

Class boundary	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Frequency	$12$	$30$	$x$	$65$	$y$	$25$	$18$

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 9 - Measures of Central Tendency>EXERCISE 1C>Q 1

The heights $($ in $cm$ $)$ of some students is given. Find the mode of the heights.

$71, 70, 70, 72, 71, 73, 71, 74, 71, 72, 72, 71, 73, 70, 72, 70, 73, 75, 71, 75, 70, 72, 75, 74, 73$

MEDIUM

10th West Bengal Board

IMPORTANT

SCHOOL MATHEMATICS Class 10>Chapter 9 - Measures of Central Tendency>EXERCISE 1C>Q 2

If the daily wage of

12

persons are

₹ 50, ₹ 60, ₹ 70, ₹ 80, ₹ 70, ₹ 90, ₹ 70, ₹ 50, ₹ 50, ₹ 100, ₹ 70, ₹ 60

. Find the mode of the wages.

Income $(₹)$	$100$	$150$	$80$	$200$	$250$	$180$
Number of persons	$24$	$26$	$16$	$20$	$6$	$30$

Find the median from the given data. Income ₹ 100 150 80 200 250 180 Number of persons 24 26 16 20 6 30

Important Questions on Measures of Central Tendency

Learn and Prepare for any exam you want !

Find the median from the given data.

Income $(₹)$ $100$ $150$ $80$ $200$ $250$ $180$

Number of persons $24$ $26$ $16$ $20$ $6$ $30$