Use graph paper for this question. A survey regarding height (in cm ) of 60 boys belonging to class 10 of a school was conducted. The following data was recorded: Height (in cm ) 135 - 140 140 - 145 145 - 150 150 - 155 155 - 160 160 - 165 165 - 170 No. of boys 4 8 20 14 7 6 1 Taking 2 cm = height of 10 cm on one axis and 2 cm = 10 boys along the other axis, draw an ogive of the above distribution. Use the graph to estimate the median.

The cumulative frequency distribution for the given data is as follows: Height (in cm ) No. of boys Cumulative frequency 135 - 140 4 4 140 - 145 8 12 145 - 150 20 32 150 - 155 14 46 155 - 160 7 53 160 - 165 6 59 165 - 170 1 60 To draw the Ogive: Plot the points ( 140 , 4 ) , ( 145 , 12 ) , ( 150 , 32 ) , ( 155 , 46 ) , ( 160 , 53 ) , ( 165 , 59 ) , ( 170 , 60 ) and ( 135 , 0 ) after drawing a kink on the x - axis near to the origin, representing that it starts from 135 instead of 0 . The Ogive for the given data is as follows: Here, n (total number of shooters) = 60 , which is even. To find the Median: ( i ) Let A be the point on y - axis representing frequency = n 2 = 30 ( i i ) Through A , we draw a horizontal line to meet the cumulative frequency curve at P . ( i i i ) Through P , draw a vertical line to meet the x - axis at Q . The abscissa of the point Q represents 149 . 5 . ∴ The required median height = 149 . 5 cm .

Use graph paper for this question. A survey regarding height (in cm ) of 60 boys belonging to class 10 of a school was conducted. The following data was recorded: Height (in cm ) 135 - 140 140 - 145 145 - 150 150 - 155 155 - 160 160 - 165 165 - 170 No. of boys 4 8 20 14 7 6 1 Taking 2 cm = height of 10 cm on one axis and 2 cm = 10 boys along the other axis, draw an ogive of the above distribution. Use the graph to estimate the lower quartile.

The cumulative frequency distribution for the given data is as follows: Height (in cm ) No. of boys Cumulative frequency 135 - 140 4 4 140 - 145 8 12 145 - 150 20 32 150 - 155 14 46 155 - 160 7 53 160 - 165 6 59 165 - 170 1 60 To draw the Ogive: Plot the points ( 140 , 4 ) , ( 145 , 12 ) , ( 150 , 32 ) , ( 155 , 46 ) , ( 160 , 53 ) , ( 165 , 59 ) , ( 170 , 60 ) and ( 135 , 0 ) after drawing a kink on the x - axis near to the origin, representing that it starts from 135 instead of 0 . The Ogive for the given data is as follows: Here, n (number of boys) = 60 , which is even. To find the Lower Quartile ( Q 1 ): ( i ) Let B be the point on y - axis representing frequency = n 4 = 15 ( i i ) Through B , we draw a horizontal line to meet the cumulative frequency curve at M . ( i i i ) Through M , draw a vertical line to meet the x - axis at N . The abscissa of the point N represents 146 . ∴ The required Lower Quartile height = 146 cm .

Use graph paper for this question. A survey regarding height (in cm ) of 60 boys belonging to class 10 of a school was conducted. The following data was recorded: Height (in cm ) 135 - 140 140 - 145 145 - 150 150 - 155 155 - 160 160 - 165 165 - 170 No. of boys 4 8 20 14 7 6 1 Taking 2 cm = height of 10 cm on one axis and 2 cm = 10 boys along the other axis, draw an ogive of the above distribution. Use the graph to estimate that if above 158 is considered as the tall boy of the class, find the number of boys in the class who are tall.

The cumulative frequency distribution for the given data is as follows: Height (in cm ) No. of boys Cumulative frequency 135 - 140 4 4 140 - 145 8 12 145 - 150 20 32 150 - 155 14 46 155 - 160 7 53 160 - 165 6 59 165 - 170 1 60 To draw the Ogive: Plot the points ( 140 , 4 ) , ( 145 , 12 ) , ( 150 , 32 ) , ( 155 , 46 ) , ( 160 , 53 ) , ( 165 , 59 ) , ( 170 , 60 ) and ( 135 , 0 ) after drawing a kink on the x - axis near to the origin, representing that it starts from 135 instead of 0 . The Ogive for the given data is as follows: To find the number of tall boys in the class: ( i ) Let D be the point on x - axis representing variate = 158 ( i i ) Through D , we draw a vertical line to meet the cumulative frequency curve at E . ( i i i ) Through E , draw a horizontal line to meet the y - axis at F . The ordinate of the point F represents 51 . ∴ The number of tall boys with height more than 158 cm = 60 - 51 = 9 .

The marks obtained by 100 students in a Mathematics test are given below: Marks 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 90 - 100 No. of students 3 7 12 17 23 14 9 6 5 4 Draw an ogive on a graph sheet and from it, determine the median.

The cumulative frequency distribution for the given data is as follows: Marks No. of students Cumulative frequency 0 - 10 3 3 10 - 20 7 10 20 - 30 12 22 30 - 40 17 39 40 - 50 23 62 50 - 60 14 76 60 - 70 9 85 70 - 80 6 91 80 - 90 5 96 90 - 100 4 100 To draw its Ogive: Plot the points ( 10 , 3 ) , ( 20 , 10 ) , ( 30 , 22 ) , ( 40 , 39 ) , ( 50 , 62 ) , ( 60 , 76 ) , ( 70 , 85 ) , ( 80 , 91 ) , ( 90 , 96 ) , ( 100 , 100 ) and ( 0 , 0 ) . The Ogive plot for the given data is as follows: Here, n (total number of students) = 100 , which is even. To find the Median: ( i ) Let A be the point on y - axis representing frequency = n 2 = 50 ( i i ) Through A , we draw a horizontal line to meet the cumulative frequency curve at P . ( i i i ) Through P , draw a vertical line to meet the x - axis at Q . The abscissa of the point Q represents 45 . ∴ The required median marks = 45 .

The marks obtained by 100 students in a Mathematics test are given below: Marks 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 90 - 100 No. of students 3 7 12 17 23 14 9 6 5 4 Draw an ogive on a graph sheet and from it, determine the lower quartile.

The cumulative frequency distribution for the given data is as follows: Marks No. of students Cumulative frequency 0 - 10 3 3 10 - 20 7 10 20 - 30 12 22 30 - 40 17 39 40 - 50 23 62 50 - 60 14 76 60 - 70 9 85 70 - 80 6 91 80 - 90 5 96 90 - 100 4 100 To draw its Ogive: Plot the points ( 10 , 3 ) , ( 20 , 10 ) , ( 30 , 22 ) , ( 40 , 39 ) , ( 50 , 62 ) , ( 60 , 76 ) , ( 70 , 85 ) , ( 80 , 91 ) , ( 90 , 96 ) , ( 100 , 100 ) and ( 0 , 0 ) . The Ogive plot for the given data is as follows: Here, n (total number of students) = 100 , which is even. To find the Lower Quartile ( Q 1 ): ( i ) Let D be the point on y - axis representing frequency = n 4 = 25 ( i i ) Through D , we draw a horizontal line to meet the cumulative frequency curve at E . ( i i i ) Through E , draw a vertical line to meet the x - axis at F . The abscissa of the point F represents 32 . ∴ The required Lower Quartile marks = 32 .

The marks obtained by 100 students in a Mathematics test are given below: Marks 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 90 - 100 No. of students 3 7 12 17 23 14 9 6 5 4 Draw an ogive on a graph sheet and from it, determine the number of students who obtained more than 85 % marks in the test.

The cumulative frequency distribution for the given data is as follows: Marks No. of students Cumulative frequency 0 - 10 3 3 10 - 20 7 10 20 - 30 12 22 30 - 40 17 39 40 - 50 23 62 50 - 60 14 76 60 - 70 9 85 70 - 80 6 91 80 - 90 5 96 90 - 100 4 100 To draw its Ogive: Plot the points ( 10 , 3 ) , ( 20 , 10 ) , ( 30 , 22 ) , ( 40 , 39 ) , ( 50 , 62 ) , ( 60 , 76 ) , ( 70 , 85 ) , ( 80 , 91 ) , ( 90 , 96 ) , ( 100 , 100 ) and ( 0 , 0 ) . The Ogive plot for the given data is as follows: To find the number of students with marks > 85 : ( i ) Let B be the point on x - axis representing variate = 85 ( i i ) Through B , we draw a vertical line to meet the cumulative frequency curve at M . ( i i i ) Through M , draw a horizontal line to meet the y - axis at N . The ordinate of the point N represents 94 . ∴ The number of students with marks more than 85 = 100 - 94 = 6 .

The marks obtained by 100 students in a Mathematics test are given below: Marks 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 90 - 100 No. of students 3 7 12 17 23 14 9 6 5 4 Draw an ogive on a graph sheet and from it, determine the number of students who did not pass in the test, if the pass percentage was 35 .

The cumulative frequency distribution for the given data is as follows: Marks No. of students Cumulative frequency 0 - 10 3 3 10 - 20 7 10 20 - 30 12 22 30 - 40 17 39 40 - 50 23 62 50 - 60 14 76 60 - 70 9 85 70 - 80 6 91 80 - 90 5 96 90 - 100 4 100 To draw its Ogive: Plot the points ( 10 , 3 ) , ( 20 , 10 ) , ( 30 , 22 ) , ( 40 , 39 ) , ( 50 , 62 ) , ( 60 , 76 ) , ( 70 , 85 ) , ( 80 , 91 ) , ( 90 , 96 ) , ( 100 , 100 ) and ( 0 , 0 ) . The Ogive plot for the given data is as follows: To find the number of students with scores < 35 : ( i ) Let C be the point on x - axis representing variate = 35 ( i i ) Through C , we draw a vertical line to meet the cumulative frequency curve at T . ( i i i ) Through T , draw a horizontal line to meet the y - axis at W . The ordinate of the point W represents 30 . ∴ The number of students with marks less than 35 = 30 .

HARD

10th ICSE

IMPORTANT

Earn 100

The monthly income of a group of $320$ employees in a company is given below:

Monthly Income (in $₹$ ) $6000 - 7000$ $7000 - 8000$ $8000 - 9000$ $9000 - 10000$ $10000 - 11000$ $11000 - 12000$ $12000 - 13000$

No. of Employees $20$ $45$ $65$ $95$ $60$ $30$ $5$

Draw an ogive of the given distribution on a graph sheet taking $2 cm = ₹ 1000$ on one axis and $2 cm = 50$ employees on the other axis. From the graph, determine that if the salary of a senior employee is above $₹ 11500$ , then find the number of senior employees in the company.

Important Questions on Measures of Central Tendency

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.6>Q 6

The monthly income of a group of $320$ employees in a company is given below:

Monthly Income (in $₹$ )	$6000 - 7000$	$7000 - 8000$	$8000 - 9000$	$9000 - 10000$	$10000 - 11000$	$11000 - 12000$	$12000 - 13000$
No. of Employees	$20$	$45$	$65$	$95$	$60$	$30$	$5$

Draw an ogive of the given distribution on a graph sheet taking $2 cm = ₹ 1000$ on one axis and $2 cm = 50$ employees on the other axis. From the graph, determine the upper quartile.

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.6>Q 7

Use graph paper for this question.

A survey regarding height (in $cm$ ) of $60$ boys belonging to class $10$ of a school was conducted. The following data was recorded:

Height (in $cm$ )	$135 - 140$	$140 - 145$	$145 - 150$	$150 - 155$	$155 - 160$	$160 - 165$	$165 - 170$
No. of boys	$4$	$8$	$20$	$14$	$7$	$6$	$1$

Taking $2 cm =$ height of $10 cm$ on one axis and $2 cm = 10$ boys along the other axis, draw an ogive of the above distribution. Use the graph to estimate the median.

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.6>Q 7

Use graph paper for this question.

A survey regarding height (in $cm$ ) of $60$ boys belonging to class $10$ of a school was conducted. The following data was recorded:

Height (in $cm$ )	$135 - 140$	$140 - 145$	$145 - 150$	$150 - 155$	$155 - 160$	$160 - 165$	$165 - 170$
No. of boys	$4$	$8$	$20$	$14$	$7$	$6$	$1$

Taking $2 cm =$ height of $10 cm$ on one axis and $2 cm = 10$ boys along the other axis, draw an ogive of the above distribution. Use the graph to estimate the lower quartile.

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.6>Q 7

Use graph paper for this question.

A survey regarding height (in $cm$ ) of $60$ boys belonging to class $10$ of a school was conducted. The following data was recorded:

Height (in $cm$ )	$135 - 140$	$140 - 145$	$145 - 150$	$150 - 155$	$155 - 160$	$160 - 165$	$165 - 170$
No. of boys	$4$	$8$	$20$	$14$	$7$	$6$	$1$

Taking $2 cm =$ height of $10 cm$ on one axis and $2 cm = 10$ boys along the other axis, draw an ogive of the above distribution. Use the graph to estimate that if above $158$ is considered as the tall boy of the class, find the number of boys in the class who are tall.

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.6>Q 8

The marks obtained by $100$ students in a Mathematics test are given below:

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$	$90 - 100$
No. of students	$3$	$7$	$12$	$17$	$23$	$14$	$9$	$6$	$5$	$4$

Draw an ogive on a graph sheet and from it, determine the median.

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.6>Q 8

The marks obtained by $100$ students in a Mathematics test are given below:

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$	$90 - 100$
No. of students	$3$	$7$	$12$	$17$	$23$	$14$	$9$	$6$	$5$	$4$

Draw an ogive on a graph sheet and from it, determine the lower quartile.

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.6>Q 8

The marks obtained by $100$ students in a Mathematics test are given below:

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$	$90 - 100$
No. of students	$3$	$7$	$12$	$17$	$23$	$14$	$9$	$6$	$5$	$4$

Draw an ogive on a graph sheet and from it, determine the number of students who obtained more than $85 %$ marks in the test.

HARD

10th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 10>Chapter 21 - Measures of Central Tendency>Exercise 21.6>Q 8

The marks obtained by $100$ students in a Mathematics test are given below:

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$	$90 - 100$
No. of students	$3$	$7$	$12$	$17$	$23$	$14$	$9$	$6$	$5$	$4$

Draw an ogive on a graph sheet and from it, determine the number of students who did not pass in the test, if the pass percentage was $35$ .

Important Questions on Measures of Central Tendency

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