Given below is a cumulative frequency distribution showing the marks secured by 50 students of a class Marks Below 20 Below 40 Below 60 Below 80 Below 100 Number of students 17 22 29 37 50 Form the frequency distribution table for the data.

Here, we above that, 17 students have scored marks below 20 i.e., it lies between class interval 0 - 20 and 22 students have scored marks below 40 , so 22 - 17 = 5 students lie in the class interval 20 - 40 continuing in the same manner, we get the complete frequency distribution table for given data, Marks Number of students 0 - 20 17 20 - 40 22 - 17 = 5 40 - 60 29 - 22 = 7 60 - 80 37 - 29 = 8 80 - 100 50 - 37 = 13

Weekly income of 600 families is tabulated below. Weekly income (in ₹ ) Number of families 0 - 1000 250 1000 - 2000 190 2000 - 3000 100 3000 - 4000 40 4000 - 5000 15 5000 - 6000 5 Total 600 Compute the median income.

First we construct a cumulative frequency table. Weekly income (in ₹ ) Number of families ( f i ) Cumulative frequency ( c f ) 0 - 1000 250 250 1000 - 2000 = med class 190 = f 250 + 190 = 440 2000 - 3000 100 440 + 100 = 540 3000 - 4000 40 540 + 40 = 580 4000 - 5000 15 580 + 15 = 595 5000 - 6000 5 595 + 5 = 600 It is given that, n = 600 ∴ n 2 = 600 2 = 300 Since, cumulative frequency 440 lies in the interval 1000 - 2000 . Here, (lower limit of the median class) n = 1000 f = 190 , c f = 250 , (class width) h = 1000 and (total observation) n = 600 ∴ Median = l + n 2 - c f f × h = 1000 + ( 300 - 250 ) 190 × 1000 = 1000 + 50 190 × 1000 = 1000 + 5000 19 = 1000 + 263 . 15 = 1263 . 15 Hence, the median income is ₹ 1263 . 15

The maximum bowling speeds, in km per hour, of 33 players at a cricket coaching centre are given as follows. Speed (in km / h ) 85 - 100 100 - 115 115 - 130 130 - 145 Number of players 11 9 8 5 Calculate the median bowling speed.

First we construct the cumulative frequency table. Speed (in km / h ) Number of players Cumulative frequency 85 - 100 11 11 100 - 115 9 11 + 9 = 20 115 - 130 8 20 + 8 = 28 130 - 145 5 28 + 5 = 33 It is given that, n = 33 ∴ n 2 = 33 2 = 16 . 5 So, the median class is 100 - 115 . Where, lower limit ( l ) = 100 , frequency ( f ) = 9 cumulative frequency ( c f ) = 11 and class width ( h ) = 15 ∴ Median = l + n 2 - c f f × h = 100 + ( 16 . 5 - 11 ) 9 × 15 = 100 + 5 . 5 × 15 9 = 100 + 82 . 5 9 = 100 + 9 . 17 = 109 . 17 Hence, the median bowling speed is 109 . 17 km / h .

The monthly income of 100 families are given as below Income (in ₹ ) Number of families 0 - 5000 8 5000 - 10000 26 10000 - 15000 41 15000 - 20000 16 20000 - 25000 3 25000 - 30000 3 30000 - 35000 2 35000 - 40000 1 Calculate the modal income.

The monthly income of 100 families are given as below Income (in ₹ ) Number of families 0 - 5000 8 5000 - 10000 26 10000 - 15000 41 15000 - 20000 16 20000 - 25000 3 25000 - 30000 3 30000 - 35000 2 35000 - 40000 1 The highest frequency is 41 , so the mode lies in the interval 10000 - 15000 . Here, l = 10000 , f m = 41 , f 1 = 26 , f 2 = 16 and h = 5000 ∴ Mode = l + f m - f 1 2 f m - f 1 - f 2 × h = 10000 + 41 - 26 2 × 41 - 26 - 16 × 5000 = 10000 + 15 82 - 42 × 5000 10000 + 15 40 × 5000 = 10000 + 15 × 125 = 10000 + 1875 = ₹ 11875 Hence, the modal income is ₹ 11875 .

The weight of coffee in 70 packets are shown in the following table Weight (in g ) Number of packets 200 - 201 12 201 - 202 26 202 - 203 20 203 - 204 9 204 - 205 2 205 - 206 1 Determine the modal weight.

The weight of coffee in 70 packets are shown in the following table Weight (in g ) Number of packets 200 - 201 12 201 - 202 26 202 - 203 20 203 - 204 9 204 - 205 2 205 - 206 1 In the given data, the highest frequency is 26 , which lies in the interval 201 - 202 Here, l = 201 , f m = 26 , f 1 = 12 , f 2 = 20 and (class width) h = 1 ∴ Mode = l + f m - f 1 2 f m - f 1 - f 2 × h = 201 + 26 - 12 2 × 26 - 12 - 20 × 1 = 201 + 14 52 - 32 = 201 + 14 20 = 201 + 0 . 7 = 201 . 7 g Hence, the modal weight is 201 . 7 g

HARD

10th CBSE

IMPORTANT

Earn 100

The following are the ages of $300$ patients getting medical treatment in a hospital on a particular day

Age (in year) $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$ $50 - 60$ $60 - 70$

Number of patients $60$ $42$ $55$ $70$ $53$ $20$

Form More than type cumulative frequency distribution.

Important Questions on Statistics and Probability

MEDIUM

10th CBSE

IMPORTANT

NCERT EXEMPLAR PROBLEMS-SOLUTIONS MATHEMATICS>Chapter 13 - Statistics and Probability>Exercise>Q 14

Given below is a cumulative frequency distribution showing the marks secured by $50$ students of a class

Marks	Below $20$	Below $40$	Below $60$	Below $80$	Below $100$
Number of students	$17$	$22$	$29$	$37$	$50$

Form the frequency distribution table for the data.

HARD

10th CBSE

IMPORTANT

NCERT EXEMPLAR PROBLEMS-SOLUTIONS MATHEMATICS>Chapter 13 - Statistics and Probability>Exercise>Q 15

Weekly income of $600$ families is tabulated below.

Weekly income (in $₹$ )	Number of families
$0 - 1000$	$250$
$1000 - 2000$	$190$
$2000 - 3000$	$100$
$3000 - 4000$	$40$
$4000 - 5000$	$15$
$5000 - 6000$	$5$
Total	$600$

Compute the median income.

HARD

10th CBSE

IMPORTANT

NCERT EXEMPLAR PROBLEMS-SOLUTIONS MATHEMATICS>Chapter 13 - Statistics and Probability>Exercise>Q 16

The maximum bowling speeds, in $km$ per hour, of $33$ players at a cricket coaching centre are given as follows.

Speed (in $km / h$ )	$85 - 100$	$100 - 115$	$115 - 130$	$130 - 145$
Number of players	$11$	$9$	$8$	$5$

Calculate the median bowling speed.

HARD

10th CBSE

IMPORTANT

NCERT EXEMPLAR PROBLEMS-SOLUTIONS MATHEMATICS>Chapter 13 - Statistics and Probability>Exercise>Q 17

The monthly income of $100$ families are given as below

Income (in $₹$ )	Number of families
$0 - 5000$	$8$
$5000 - 10000$	$26$
$10000 - 15000$	$41$
$15000 - 20000$	$16$
$20000 - 25000$	$3$
$25000 - 30000$	$3$
$30000 - 35000$	$2$
$35000 - 40000$	$1$

Calculate the modal income.

HARD

10th CBSE

IMPORTANT

NCERT EXEMPLAR PROBLEMS-SOLUTIONS MATHEMATICS>Chapter 13 - Statistics and Probability>Exercise>Q 18

The weight of coffee in $70$ packets are shown in the following table

Weight (in $g$ )	Number of packets
$200 - 201$	$12$
$201 - 202$	$26$
$202 - 203$	$20$
$203 - 204$	$9$
$204 - 205$	$2$
$205 - 206$	$1$

Determine the modal weight.

EASY

10th CBSE

IMPORTANT

NCERT EXEMPLAR PROBLEMS-SOLUTIONS MATHEMATICS>Chapter 13 - Statistics and Probability>Exercise>Q 19

Two dice are thrown at the same time. Find the probability of getting same number on both dice.

EASY

10th CBSE

IMPORTANT

NCERT EXEMPLAR PROBLEMS-SOLUTIONS MATHEMATICS>Chapter 13 - Statistics and Probability>Exercise>Q 19

Two dice are thrown at the same time. Find the probability of getting different numbers on both dice.

EASY

10th CBSE

IMPORTANT

NCERT EXEMPLAR PROBLEMS-SOLUTIONS MATHEMATICS>Chapter 13 - Statistics and Probability>Exercise>Q 20

Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is $7 ?$

Age (in year)	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$
Number of patients	$60$	$42$	$55$	$70$	$53$	$20$

The following are the ages of 300 patients getting medical treatment in a hospital on a particular day Age (in year) 10-20 20-30 30-40 40-50 50-60 60-70 Number of patients 60 42 55 70 53 20 Form More than type cumulative frequency distribution.

Important Questions on Statistics and Probability

Learn and Prepare for any exam you want !

The following are the ages of $300$ patients getting medical treatment in a hospital on a particular day

Age (in year) $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$ $50 - 60$ $60 - 70$

Number of patients $60$ $42$ $55$ $70$ $53$ $20$

Form More than type cumulative frequency distribution.