If the median of the following frequency distribution is 32 . 5 . Find the values of f 1 and f 2 . Class 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 Frequency f 1 5 9 12 f 2 3 2 40

Find the Cumulative Frequency of the given data. class Frequency f Cumulative Frequency c f 0 - 10 f 1 f 1 10 - 20 5 f 1 + 5 20 - 30 9 f 1 + 14 30 - 40 12 f 1 + 26 40 - 50 f 2 f 1 + f 2 + 26 50 - 60 3 f 1 + f 2 + 29 60 - 70 2 f 1 + f 2 + 31 N = ∑ f = 40 Sum of Cumulative Frequency is f 1 + f 2 + 31 = 40 ⇒ f 1 + f 2 = 9 . . . . . . . ( 1 ) Now, The median 32 . 5 is lies between 30 - 40 . Hence, median class is 30 - 40 . ∴ l = 30 , N 2 = 40 2 = 20 , h = 10 , f = 12 , cumulative frequency of preceding class ( cf ) = 14 + f 1 . Now, median is given as, M = l + ( N 2 - cf ) f × h 32 . 5 = 30 + ( 20 - ( 14 + f 1 ) 12 × 10 2 . 5 = ( 60 - 10 f 1 ) 12 30 = 60 - 10 f 1 f 1 = 30 10 f 1 = 3 From equation ( 1 ) , we get f 2 = 9 - f 1 f 2 = 9 - 3 f 2 = 6 Hence, the value of f 1 is 3 and f 2 is 6 .

The following table gives production yield per hectare of wheat of 100 farms of a village Production yield kg / hec 40 - 45 45 - 50 50 - 55 55 - 60 60 - 65 65 - 70 Number of farms 4 6 16 20 30 24 Change the distribution to a 'more than type' distribution and draw its ogive.

The cumulative frequency distribution table by more than type is as below: Production yield kg / hec Number of farms f i Production yield kg / hec Cumulative frequency c . f . 40 - 45 4 More than 40 4 + 96 = 100 45 - 50 6 More than 45 6 + 90 = 96 50 - 55 16 More than 50 16 + 74 = 90 55 - 60 20 More than 55 20 + 54 = 74 60 - 65 30 More than 60 30 + 24 = 54 65 - 70 24 More than 65 24 Mark lower class limits on x - axis and cumulative frequency on y - axis. We plot the points 40 , 100 , 45 , 96 , 50 , 90 , 55 , 74 , 60 , 54 , and 65 , 24 . Joining the above points by line segments, the cumulative frequency polygon is as shown below:

The median of the following data is 525 . Find the values of x and y , if total frequency is 100 . Class 0 - 100 100 - 200 200 - 300 300 - 400 400 - 500 500 - 600 600 - 700 700 - 800 800 - 900 900 - 1000 Frequency 2 5 x 12 17 20 y 9 7 4

Cumulative frequency for the given data; Class interval Frequency f Cumulative frequency CF 0 - 100 2 2 100 - 200 5 7 200 - 300 x x + 7 300 - 400 12 x + 19 400 - 500 17 x + 36 500 - 600 20 x + 56 600 - 700 y x + y + 56 700 - 800 9 x + y + 65 800 - 900 7 x + y + 72 900 - 1000 4 x + y + 76 total Σ f = 76 + x + y = 100 Given that the median is 525 . So median class is 500 - 600 Now median = l + N 2 - C F f × h where l = 500 , h = 100 , N = 100 , C F = 36 + x , f = 20 so, 525 = 500 + 100 2 - ( 36 + x ) 20 × 100 ⇒ 525 - 500 = ( 50 - ( 36 + x ) ) × 5 ⇒ 25 = ( 14 - x ) × 5 ⇒ x = 9 Also, Σ f = 76 + x + y = 100 ⇒ 9 + y = 100 - 76 ⇒ y = 15 Hence, x = 9 and y = 15

Embibe Experts Solutions for Chapter: Statistics, Exercise 1: CBSE-2018

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Embibe Experts Mathematics Solutions for Exercise - Embibe Experts Solutions for Chapter: Statistics, Exercise 1: CBSE-2018

Attempt the free practice questions on Chapter 14: Statistics, Exercise 1: CBSE-2018 with hints and solutions to strengthen your understanding. EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS solutions are prepared by Experienced Embibe Experts.

Questions from Embibe Experts Solutions for Chapter: Statistics, Exercise 1: CBSE-2018 with Hints & Solutions

HARD

10th CBSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Statistics>CBSE-2018>Q 3

The mean of the following distribution is $18$ . Find the frequency $f$ of the class $19 - 21$ .

Class	$11 - 13$	$13 - 15$	$15 - 17$	$17 - 19$	$19 - 21$	$21 - 23$	$23 - 25$
Frequency	$3$	$6$	$9$	$13$	$f$	$5$	$4$

MEDIUM

10th CBSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Statistics>CBSE-2019>Q 5

Find the mode of the following frequency distribution.

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$
Frequency	$8$	$10$	$10$	$16$	$12$	$6$	$7$

MEDIUM

10th CBSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Statistics>CBSE-2019>Q 6

If the median of the following frequency distribution is $32.5$ . Find the values of $f_{1}$ and $f_{2}$ .

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Frequency	$f_{1}$	$5$	$9$	$12$	$f_{2}$	$3$	$2$	$40$

EASY

10th CBSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Statistics>CBSE-2020>Q 8

If the mean of the first $n$ natural numbers is $15$ , then find $n$ .

MEDIUM

10th CBSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Statistics>CBSE-2020>Q 9

Find the mean of the following distribution:

Class	$3 - 5$	$5 - 7$	$7 - 9$	$9 - 11$	$11 - 13$
Frequency	$5$	$10$	$10$	$7$	$8$

EASY

10th CBSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Statistics>CBSE-2020>Q 10

Find the mode of the following distribution:

Class:	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$	$100 - 120$	$120 - 140$
Frequency:	$6$	$8$	$10$	$12$	$6$	$5$	$3$

MEDIUM

10th CBSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Statistics>CBSE-2020>Q 11

The following table gives production yield per hectare of wheat of $100$ farms of a village

Production yield $(kg / hec)$	$40 - 45$	$45 - 50$	$50 - 55$	$55 - 60$	$60 - 65$	$65 - 70$
Number of farms	$4$	$6$	$16$	$20$	$30$	$24$

Change the distribution to a 'more than type' distribution and draw its ogive.

MEDIUM

10th CBSE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Statistics>CBSE-2020>Q 12

The median of the following data is $525$ . Find the values of $x$ and $y$ , if total frequency is $100$ .

Class	$0 - 100$	$100 - 200$	$200 - 300$	$300 - 400$	$400 - 500$	$500 - 600$	$600 - 700$	$700 - 800$	$800 - 900$	$900 - 1000$
Frequency	$2$	$5$	$x$	$12$	$17$	$20$	$y$	$9$	$7$	$4$

Embibe Experts Solutions for Chapter: Statistics, Exercise 1: CBSE-2018

Embibe Experts Mathematics Solutions for Exercise - Embibe Experts Solutions for Chapter: Statistics, Exercise 1: CBSE-2018

Questions from Embibe Experts Solutions for Chapter: Statistics, Exercise 1: CBSE-2018 with Hints & Solutions

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