Draw less than ogive and more than ogive for following distribution giving 400 telephone calls according to their duration in seconds. Duration (in s ) 0 - 30 30 - 60 60 - 90 90 - 120 120 - 150 150 - 180 180 - 210 Number of calls 25 75 50 25 150 50 25 Hence, find the median of the distribution and verify it by using formula. Also find Q 1 , Q 3 , D 9 , P 4 and P 40 from graph.

Less than type cumulative frequency distribution is below: Duration (in s ) less than or equal to 30 60 90 120 150 180 210 Number of calls C . f 25 100 150 175 325 375 400 Take: 1cm along x -axis = 30 sec. 1 cm along y -axis = 50 calls Plot the point and join them by free hand curve : ( 30 , 25 ) , ( 60 , 100 ) , ( 90 , 150 ) , ( 120 , 175 ) , ( 150 , 325 ) , ( 180 , 375 ) , ( 210 , 400 ) and 0 , 0 More than type cumulative frequency distribution is below: Duration (in sec ) 0 20 60 90 120 150 180 Number of calls C . f 400 375 300 250 225 75 25 Plot the points ( 0 , 400 ) , ( 30 , 375 ) , ( 60 , 300 ) , ( 90 , 250 ) , ( 120 , 225 ) , ( 150 , 75 ) , ( 180 , 25 ) and 210 , 0 .and join them by free hand curve.Both curves intersect at P . From this draw ⊥ P M on x - axis. the abscissa of point M gives required median = 125 . To find Q 1 : Q 1 is n 4 th value i.e. 400 4 th value i.e. 100 th item The x th value of the 100 th observation is 60 , ∴ Q 1 = 60 To find Q 3 : Q 3 is 3 n 4 th item i.e. 3 × 400 4 th item i.e. 300 th item Thus x th value of 300th item is 145 sec. To find D 9 : D 9 = 9 × n 10 th item i.e. 9 × 400 10 th item i . e , 360 th item From ogive x th value of 360 th item = 171 sec To find P 4 : P 4 = 4 n 100 th item i.e. 4 × 400 100 th item , 16 th item From ogive x th value of 16 th item is 19 sec To find P 40 : P 40 = 40 n 100 th item i.e. 40 × 400 100 th item , 160 th item From ogive x - value of 160 th item is 102 sec.

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

Author:M L Aggarwal

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

Attempt the practice questions on Chapter 1: Statistics, Exercise 5: EXERCISE with hints and solutions to strengthen your understanding. Understanding ISC Mathematics Class 11 Volume 2 solutions are prepared by Experienced Embibe Experts.

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

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 1 - Statistics>EXERCISE>Q 1

The following table shows the distribution of the heights of a group of workers in a factory:

Height (in $cm$ )	$150 - 155$	$155 - 160$	$160 - 165$	$165 - 170$	$170 - 175$	$175 - 180$	$180 - 185$
Number of workers	$6$	$12$	$18$	$20$	$13$	$8$	$6$

Convert the distribution to more than cumulative frequency distribution and draw its ogive. Hence, obtain the median from the graph.

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 1 - Statistics>EXERCISE>Q 2

Attempt this question on a graph paper. The table shows the distribution of the marks obtained by $160$ students in a test:

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Number of Students	$12$	$20$	$30$	$38$	$24$	$16$	$12$	$8$

Construct more than type cumulative frequency table and draw its ogive. From the ogive, determine the median marks.

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 1 - Statistics>EXERCISE>Q 6

$100$ students in a school have heights as tabulated below:

Height (in $cm$ )	$121 - 130$	$131 - 140$	$141 - 150$	$151 - 160$	$161 - 170$	$171 - 180$
Number of pupils	$12$	$16$	$30$	$20$	$14$	$8$

Draw the ogive for the above data and from it determine the median (use graph paper.)

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 1 - Statistics>EXERCISE>Q 8

Draw an ogive for the following data:

Class	$1 - 100$	$101 - 200$	$201 - 300$	$301 - 400$	$401 - 500$	$501 - 600$	$601 - 700$	$701 - 800$
Frequency	$23$	$25$	$35$	$60$	$45$	$39$	$25$	$16$

Estimate the median from your graph.

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 1 - Statistics>EXERCISE>Q 11

The table shows the frequency distribution of $weights$ of $80$ apples selected at random from a big consignment.

$Weight (g)$	$110 - 119$	$120 - 129$	$130 - 139$	$140 - 149$	$150 - 159$	$160 - 169$	$170 - 179$	$180 - 189$
Frequency	$5$	$7$	$12$	$20$	$16$	$10$	$7$	$3$

Draw both cumulative (less than) and cumulative (more than) ogives on a graph paper and determine the median $weight$ of apples from the point of intersection of these two curves.

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 1 - Statistics>EXERCISE>Q 12

The annual profits earned by $30$ shops of a shopping complex in a locality give rise to the following distribution.

Profit (in lakhs in $₹$ ) more than or equal to	$5$	$10$	$15$	$20$	$25$	$30$	$35$
Number of shops $(c . f)$	$30$	$28$	$16$	$14$	$10$	$7$	$3$

Draw both ogives for the above data.Hence, obtain median profit.

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 1 - Statistics>EXERCISE>Q 13

Draw less than ogive and more than ogive for following distribution giving $400$ telephone calls according to their duration in seconds.

Duration (in $s$ )	$0 - 30$	$30 - 60$	$60 - 90$	$90 - 120$	$120 - 150$	$150 - 180$	$180 - 210$
Number of calls	$25$	$75$	$50$	$25$	$150$	$50$	$25$

Hence, find the median of the distribution and verify it by using formula. Also find $Q_{1}, Q_{3,} D_{9}, P_{4} and P_{40}$ from graph.

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

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

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

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