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.

An examination is taken at three centres each of which has 100 candidates. The mean marks and standard deviation for each centre are given below: 1st centre 45 9 . 6 2nd centre 50 10 . 8 3rd centre 43 9 . 0 Calculate the mean and standard deviation of all 300 candidates.

Given that, n 1 = n 2 = n 3 = 100 ; x ¯ 1 = 45 ; x ¯ 2 = 50 ; x ¯ 3 = 43 ; σ 1 = 9 . 6 ; σ 2 = 10 . 8 ; σ 3 = 9 . 0 We know that, combined mean x ¯ = n 1 x ¯ 1 + n 2 x ¯ 2 + n 3 x ¯ 3 n 1 + n 2 + n 3 x ¯ = 100 × 45 + 100 × 50 + 100 × 43 100 + 100 + 100 = 100 ( 45 + 50 + 43 ) 300 = 138 3 = 46 d 1 = x ¯ - x ¯ 1 = | 46 - 45 | = 1 d 2 = x ¯ - x ¯ 2 = | 46 - 50 | = 4 d 3 = x ¯ - x ¯ 3 = | 46 - 43 | = 3 We know that, combined variance σ 2 = n 1 d 1 2 + n 2 d 2 2 + n 3 d 3 2 + n 1 σ 1 2 + n 2 σ 2 2 + n 3 σ 3 2 n 1 + n 2 + n 3 = 100 × 1 + 100 × 16 + 100 × 9 + 100 × ( 9 . 6 ) 2 + 100 × ( 10 . 8 ) 2 + 100 × 81 100 + 100 + 100 = 100 ( 1 + 16 + 9 + 92 . 16 + 116 . 64 + 81 ) 300 = 315 . 8 3 = 105 . 27 ∴ S . D σ = 10 . 26

HARD

11th ICSE

IMPORTANT

Earn 100

$100$ 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.)

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Important Questions on Statistics

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.

MEDIUM

11th ICSE

IMPORTANT

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

A shopkeeper mixes a batch of

200

apples of mean mass

150 g

and standard deviation

30 g

with another batch of

300

apples of mean mass

100 g

and standard deviation

20 g

Find the mean and standard deviation for the combined batch of

500

apples.

EASY

11th ICSE

IMPORTANT

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

For a group containing

100

observations, the mean and standard deviation are

8

and

\sqrt{10.5}

. For

50

observations selected from these

100

, the mean and standard deviation are

10

and

2

respectively. Find the arithmetic mean and standard deviation of the other half.

EASY

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 1 - Statistics>CHAPTER TEST>Q 3

An examination is taken at three centres each of which has 100 candidates. The mean marks and standard deviation for each centre are given below:

1st centre	$45$	$9.6$
2nd centre	$50$	$10.8$
3rd centre	$43$	$9.0$

Calculate the mean and standard deviation of all 300 candidates.

EASY

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 1 - Statistics>CHAPTER TEST>Q 4

Three consecutive prime numbers with median

7

are _____ , _____ , _____ .

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

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.)

Important Questions on Statistics

Learn and Prepare for any exam you want !

$100$ 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.)