For the following distribution, draw a 'more than ogive' and hence find the median: Class 0 - 30 30 - 60 60 - 90 90 - 120 120 - 150 Frequency 25 20 35 28 42

Class Frequency Upper class limits Cumulative frequency c . f 0 - 30 25 More than 0 150 30 - 60 20 More than 30 125 60 - 90 35 More than 60 105 90 - 120 28 More than 90 70 120 - 150 42 More than 120 42 Plot the points 0 , 150 , 30 , 125 , 60 , 105 , 90 , 70 , 120 , 42 to obtain the required ogive. The median will be corresponding x - coordinate of the point whose ordinate is N 2 = 150 2 = 75 . From this point draw a line perpendicular to x - axis. The point of intersection of perpendicular with the x - axis determines the median of the data. Thus, median is 90 (approx).

Draw a more than ogive for the following distribution and hence, find its median. Class 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 Frequency 25 15 10 6 24 12 8

Class interval frequency More than Cumulative frequency 20 - 30 25 20 100 30 - 40 15 30 75 40 - 50 10 40 60 50 - 60 6 50 50 60 - 70 24 60 44 70 - 80 12 70 20 80 - 90 8 80 8 Now we will plot the points corresponding to the ordered pairs 20 , 100 , 30 , 75 , 40 , 60 , 50 , 50 , 60 , 44 , 70 , 20 , 80 , 8 and join all the points by smooth curve. Now, n 2 = 100 2 = 50 From this point draw a line perpendicular to x - axis. The point of intersection of perpendicular with the x - axis determines the median of the data. Thus, median is 50 .

The marks obtained by 100 students of a class in an examination are given below: Marks 0 - 5 5 - 10 10 - 15 15 - 20 20 - 25 25 - 30 30 - 35 35 - 40 40 - 45 45 - 50 Number of students 2 5 6 8 10 25 20 18 4 2 Draw a 'less than type' cumulative frequency curve (ogive). Hence, find the median.

Marks Number of students Marks less than Cumulative frequency 0 - 5 2 Less than 5 2 5 - 10 5 Less than 10 7 10 - 15 6 Less than 15 13 15 - 20 8 Less than 20 21 20 - 25 10 Less than 25 31 25 - 30 25 Less than 30 56 30 - 35 20 Less than 35 76 35 - 40 18 Less than 40 94 40 - 45 4 Less than 45 98 45 - 50 2 Less than 50 100 Now we will plot the points corresponding to the ordered pairs 5 , 2 , 10 , 7 , 15 , 13 , 20 , 21 , 25 , 31 , 30 , 56 , 35 , 76 , 40 , 94 , 45 , 98 , 50 , 100 and join all the points by smooth curve. Now, n 2 = 100 2 = 50 on y - axis. From this point draw a perpendicular to x - axis. The point of intersection of perpendicular with the x - axis determines the median of the data. Thus, median = 28 . 8 .

A school held sports day in which 150 students participated. Ages of students are given in the following frequency distribution: Age (in years) Number of students More than or equal to 5 150 More than or equal to 7 136 More than or equal to 9 110 More than or equal to 11 85 More than or equal to 13 65 More than or equal to 15 43 More than or equal to 17 15 For the above data, draw a 'more than type' ogive and from the curve, find median. Verify it by actual calculation.

Age (in years) Number of students Class intervals Frequency f Cumulative frequency c f More than or equal to 5 150 5 - 7 14 14 More than or equal to 7 136 7 - 9 26 40 More than or equal to 9 110 9 - 11 25 65 More than or equal to 11 85 11 - 13 20 85 More than or equal to 13 65 13 - 15 22 107 More than or equal to 15 43 15 - 17 28 135 More than or equal to 17 15 17 - 19 15 150 Total n = ∑ f = 150 In order to find the median we first locate the point corresponding to N 2 = 150 2 = 75 t h student on y - axis. From this point draw a line parallel to x - axis cutting the curve at a point and from this point draw a line parallel to y - axis meeting x - axis at point 12 . Hence median is 12 . Verification: Now, n 2 = 150 2 = 75 Thus, median class is 11 - 13 . So, median = l + n 2 - c f f × h = 11 + 75 - 65 20 × 2 = 11 + 1 = 12 Thus, median is 12 years.

Draw more than type ogive and less than type ogive for the following data: Classes 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 Frequency 8 7 5 10 5 Also, find its median.

Classes Cumulative frequency ( c . f ) Classes Cumulative frequency ( c . f ) Less than 10 8 More than 0 35 Less than 20 15 More than 10 27 Less than 30 20 More than 20 20 Less than 40 30 More than 30 15 Less than 50 35 More than 40 5 Now we will draw a line perpendicular to x - axis from the point where the two types of cumulative frequency curves intersect and hence the required point on x - axis represents median which is 25 . Thus, median is 25 .

M L Aggarwal Solutions for Chapter: Statistics, Exercise 5: Exercise 15.5

Author:M L Aggarwal

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Chapter: Statistics, Exercise 5: Exercise 15.5

Attempt the free practice questions on Chapter 15: Statistics, Exercise 5: Exercise 15.5 with hints and solutions to strengthen your understanding. CBSE Syllabus Standard Mathematics for Class X solutions are prepared by Experienced Embibe Experts.

Questions from M L Aggarwal Solutions for Chapter: Statistics, Exercise 5: Exercise 15.5 with Hints & Solutions

MEDIUM

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 15 - Statistics>Exercise 15.5>Q 2

Change the following distribution to a 'more than type' distribution. Hence, draw 'more than type' ogive for this distribution:

Class interval	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$
Frequency	$10$	$8$	$12$	$24$	$6$	$25$	$15$

MEDIUM

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 15 - Statistics>Exercise 15.5>Q 3

For the following distribution, draw a 'more than ogive' and hence find the median:

Class	$0 - 30$	$30 - 60$	$60 - 90$	$90 - 120$	$120 - 150$
Frequency	$25$	$20$	$35$	$28$	$42$

MEDIUM

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 15 - Statistics>Exercise 15.5>Q 4

Draw a more than ogive for the following distribution and hence, find its median.

Class	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$
Frequency	$25$	$15$	$10$	$6$	$24$	$12$	$8$

MEDIUM

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 15 - Statistics>Exercise 15.5>Q 5

The marks obtained by $100$ students of a class in an examination are given below:

Marks	$0 - 5$	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$	$40 - 45$	$45 - 50$
Number of students	$2$	$5$	$6$	$8$	$10$	$25$	$20$	$18$	$4$	$2$

Draw a 'less than type' cumulative frequency curve (ogive). Hence, find the median.

HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 15 - Statistics>Exercise 15.5>Q 6

A school held sports day in which $150$ students participated. Ages of students are given in the following frequency distribution:

Age (in years)	Number of students
More than or equal to $5$	$150$
More than or equal to $7$	$136$
More than or equal to $9$	$110$
More than or equal to $11$	$85$
More than or equal to $13$	$65$
More than or equal to $15$	$43$
More than or equal to $17$	$15$

For the above data, draw a 'more than type' ogive and from the curve, find median.

Verify it by actual calculation.

MEDIUM

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 15 - Statistics>Exercise 15.5>Q 7

Draw more than type ogive and less than type ogive for the following data:

Classes	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
Frequency	$8$	$7$	$5$	$10$	$5$

Also, find its median.

M L Aggarwal Solutions for Chapter: Statistics, Exercise 5: Exercise 15.5

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Chapter: Statistics, Exercise 5: Exercise 15.5

Questions from M L Aggarwal Solutions for Chapter: Statistics, Exercise 5: Exercise 15.5 with Hints & Solutions

Learn and Prepare for any exam you want !