From the following frequency distribution, find: the median. Variate 15 18 20 22 25 27 30 Frequency 4 6 8 9 7 8 6

Given, We write the distribution in the cumulative frequency table. Variate Frequency f Cumulative frequency 15 4 4 18 6 10 20 8 18 22 9 27 25 7 34 27 8 42 30 6 48 Here the total number of observations are 48 which is even. So, median = n 2 th term + n 2 + 1 th term 2 = 48 2 th term + 48 2 + 1 th term 2 = 24 th term + 24 + 1 th term 2 = 24 th term + 25 th term 2 = 1 2 22 + 22 [ Since 18 th to 27 th observation is 22 ] = 1 2 × 44 = 22 Hence, the median of the given data is 22 .

From the following frequency distribution, find: lower quartile. Variate 15 18 20 22 25 27 30 Frequency 4 6 8 9 7 8 6

Given, We write the distribution in the cumulative frequency table. Variate Frequency f Cumulative frequency 15 4 4 18 6 10 20 8 18 22 9 27 25 7 34 27 8 42 30 6 48 Here the total number of observations are 48 which is even. So, lower quartile, Q 1 = n 4 th term = 48 4 th term = 12 th term [ Since 10 th to 18 th observation is 20 ] = 20 Therefore, the lower quartile is 20 .

From the following frequency distribution, find: upper quartile. Variate 15 18 20 22 25 27 30 Frequency 4 6 8 9 7 8 6

Given, We write the distribution in the cumulative frequency table. Variate Frequency f Cumulative frequency 15 4 4 18 6 10 20 8 18 22 9 27 25 7 34 27 8 42 30 6 48 Here the total number of observations are 48 which is even. So, upper quartile, Q 3 = 3 n 4 th term = 3 × 48 4 th term = 3 × 12 th term = 36 th term [ Since 34 th to 42 th observation is 27 ] = 27 Therefore, the upper quartile is 27 .

From the following frequency distribution, find: inter quartile range. Variate 15 18 20 22 25 27 30 Frequency 4 6 8 9 7 8 6

Given, We write the distribution in the cumulative frequency table. Variate Frequency f Cumulative frequency 15 4 4 18 6 10 20 8 18 22 9 27 25 7 34 27 8 42 30 6 48 Here the total number of observations are 48 which is even. We know that, Upper quartile, Q 3 = 3 n 4 th term Q 3 = 3 × 48 4 th term Q 3 = 3 × 12 th term Q 3 = 36 th term [ Since 34 th to 42 th observation is 27 ] Q 3 = 27 We know that, Lower quartile, Q 1 = n 4 th term Q 1 = 48 4 th term Q 1 = 12 th term [ Since 10 th to 18 th observation is 20 ] Q 1 = 20 Interquartile range = Q 3 - Q 1 = 27 - 20 = 7 Therefore, the interquartile range is 7 .

For the following frequency distribution, find: the median. Variate 25 31 34 40 45 48 50 60 Frequency 3 8 10 15 10 9 6 2

Given, We write the distribution in the cumulative frequency table. Variate Frequency f Cumulative frequency 25 3 3 31 8 11 34 10 21 40 15 36 45 10 46 48 9 55 50 6 61 60 2 63 Here, the number of observations n = 63 which is odd So, median = n + 1 2 th term = 63 + 1 2 th term = 64 2 th term = 32 th term [ Since 21 th to 36 th observation is 40 ] = 40 Hence, the median of the given data is 40 .

For the following frequency distribution, find: lower quartile. Variate 25 31 34 40 45 48 50 60 Frequency 3 8 10 15 10 9 6 2

Given, We write the distribution in the cumulative frequency table. Variate Frequency f Cumulative frequency 25 3 3 31 8 11 34 10 21 40 15 36 45 10 46 48 9 55 50 6 61 60 2 63 Here, the number of observations n = 63 which is odd Lower quartile, Q 1 = n + 1 4 th term = 63 + 1 4 th term = 64 4 th term = 16 th term [ Since 11 th to 21 th observation is 34 ] = 34 Hence, the lower quartile is 34 .

For the following frequency distribution, find: upper quartile. Variate 25 31 34 40 45 48 50 60 Frequency 3 8 10 15 10 9 6 2

Given, We write the distribution in the cumulative frequency table. Variate Frequency f Cumulative frequency 25 3 3 31 8 11 34 10 21 40 15 36 45 10 46 48 9 55 50 6 61 60 2 63 Here, the number of observations n = 63 which is odd Upper quartile, Q 3 = 3 n + 1 4 th term = 3 × 63 + 1 4 th term = 3 × 64 4 th term = 3 × 16 th term = 48 th term [ Since 46 th to 55 th observation is 48 ] = 48 Hence, the upper quartile is 48 .

M L Aggarwal Solutions for Exercise 2: Exercise 21.2

Author:M L Aggarwal

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Exercise 2: Exercise 21.2

Attempt the practice questions from Exercise 2: Exercise 21.2 with hints and solutions to strengthen your understanding. Understanding ICSE Mathematics Class 10 solutions are prepared by Experienced Embibe Experts.

Questions from M L Aggarwal Solutions for Exercise 2: Exercise 21.2 with Hints & Solutions

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.2>Q 9

The daily wages (in rupees) of $= 15^{th} term$ workers are $41, 21, 38, 27, 31, 45, 23, 26, 29, 30, 28, 25, 35, 42, 47, 53, 29, 31, 35, 53, 29, 31, 35$ . Find: inter quartile range.

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.2>Q 10

From the following frequency distribution, find: the median.

Variate	$15$	$18$	$20$	$22$	$25$	$27$	$30$
Frequency	$4$	$6$	$8$	$9$	$7$	$8$	$6$

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.2>Q 10

From the following frequency distribution, find: lower quartile.

Variate	$15$	$18$	$20$	$22$	$25$	$27$	$30$
Frequency	$4$	$6$	$8$	$9$	$7$	$8$	$6$

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.2>Q 10

From the following frequency distribution, find: upper quartile.

Variate	$15$	$18$	$20$	$22$	$25$	$27$	$30$
Frequency	$4$	$6$	$8$	$9$	$7$	$8$	$6$

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.2>Q 10

From the following frequency distribution, find: inter quartile range.

Variate	$15$	$18$	$20$	$22$	$25$	$27$	$30$
Frequency	$4$	$6$	$8$	$9$	$7$	$8$	$6$

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.2>Q 11

For the following frequency distribution, find: the median.

Variate	$25$	$31$	$34$	$40$	$45$	$48$	$50$	$60$
Frequency	$3$	$8$	$10$	$15$	$10$	$9$	$6$	$2$

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.2>Q 11

For the following frequency distribution, find: lower quartile.

Variate	$25$	$31$	$34$	$40$	$45$	$48$	$50$	$60$
Frequency	$3$	$8$	$10$	$15$	$10$	$9$	$6$	$2$

MEDIUM

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.2>Q 11

For the following frequency distribution, find: upper quartile.

Variate	$25$	$31$	$34$	$40$	$45$	$48$	$50$	$60$
Frequency	$3$	$8$	$10$	$15$	$10$	$9$	$6$	$2$

M L Aggarwal Solutions for Exercise 2: Exercise 21.2

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Exercise 2: Exercise 21.2

Questions from M L Aggarwal Solutions for Exercise 2: Exercise 21.2 with Hints & Solutions

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