The daily expenditure of 100 families are given as under: Expenditure 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 Number of families 14 ? 27 ? 15 The median and mode for the distribution are ₹ 26 . 67 and ₹ 29 respectively. Calculate the missing frequencies.

Here, it is given that median is ₹ 26 . 67 . And, N = 100 . If we prepare the cumulative frequency table, we get Expenditure Number of families ( f ) Cumulative frequency ( c f ) 0 - 10 14 14 10 - 20 x 14 + x 20 - 30 27 41 + x 30 - 40 y 41 + x + y 40 - 50 15 56 + x + y We know N = 100 . So, N 2 = 50 . Since, Median ₹ 26 . 67 lies in the class 20 - 30 , thus the median class is 20 - 30 . So, l = 20 , h = 10 , f = 27 and C = 14 + x . Therefore, median = l + N 2 - C f × h . ⇒ 26 . 67 = 20 + 50 - 14 - x 27 × 10 ⇒ 26 . 67 = 20 + 360 - 10 x 27 ⇒ 6 . 67 = 360 - 10 x 27 ⇒ 180 = 360 - 10 x ⇒ 10 x = 360 - 180 ⇒ x = 180 10 ∴ x = 18 Now we know that 56 + x + y = 100 Put x = 18 , we get 56 + 18 + y = 100 ⇒ y = 100 - 74 ∴ y = 26 So, the missing frequencies are 18 and 26 .

H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Statistics, Exercise 5: EXERCISE

Author:H K Dass, Rama Verma & Bhagwat Swarup Sharma

H K Dass Mathematics Solutions for Exercise - H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Statistics, Exercise 5: EXERCISE

Attempt the free practice questions on Chapter 14: Statistics, Exercise 5: EXERCISE with hints and solutions to strengthen your understanding. New Mathematics for Class X solutions are prepared by Experienced Embibe Experts.

Questions from H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Statistics, Exercise 5: EXERCISE with Hints & Solutions

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 14 - Statistics>EXERCISE>Q 1

Determine the median from the following data:

Wages (in $₹$ )	No. of workers	Wages (in $₹$ )	No. of workers
$20 - 40$	$4$	$100 - 120$	$12$
$40 - 60$	$6$	$120 - 140$	$7$
$60 - 80$	$10$	$140 - 160$	$3$
$80 - 100$	$16$

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 14 - Statistics>EXERCISE>Q 2

Calculate the value of median:

Class	$0 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$	$40 - 45$	$45 - 50$
Frequency	$1$	$2$	$5$	$7$	$10$	$7$	$5$	$2$	$1$

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 14 - Statistics>EXERCISE>Q 3

Draw an ogive for the following distribution. Read the median from the graph, and verify the result by calculation. How many workers earned wages between $₹ 60$ and $₹ 72$ ?

Weekly wages (in $₹$ )	No. of workers	Weekly wages (in $₹$ )	No. of workers
$50 - 55$	$6$	$70 - 75$	$16$
$55 - 60$	$10$	$75 - 80$	$12$
$60 - 65$	$22$	$80 - 100$	$15$
$65 - 70$	$30$

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 14 - Statistics>EXERCISE>Q 4

The following table shows the marks obtained by $100$ candidates in an examination. Calculate the median (upto two decimal places).

Marks	$1 - 10$	$11 - 20$	$21 - 30$	$31 - 40$	$41 - 50$	$51 - 60$
No. of candidates	$3$	$16$	$26$	$31$	$16$	$8$

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 14 - Statistics>EXERCISE>Q 5

Find the median of the following table:

Marks	No. of students	Marks	No. of students
Below $10$	$15$	Below $50$	$96$
Below $20$	$35$	Below $60$	$127$
Below $30$	$60$	Below $70$	$198$
Below $40$	$84$	Below $80$	$250$

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 14 - Statistics>EXERCISE>Q 6

Following in the distribution of I.Q. of $100$ students. Find the median I.Q.

I.Q.	$55 - 64$	$65 - 74$	$75 - 84$	$85 - 94$	$95 - 104$	$105 - 114$	$115 - 124$	$125 - 134$	$135 - 144$
Frequency	$1$	$2$	$9$	$22$	$33$	$22$	$8$	$2$	$1$

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 14 - Statistics>EXERCISE>Q 7

The daily expenditure of $100$ families are given as under:

Expenditure	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
Number of families	$14$	$?$	$27$	$?$	$15$

The median and mode for the distribution are

₹ 26.67

and

₹ 29

respectively. Calculate the missing frequencies.

H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Statistics, Exercise 5: EXERCISE

H K Dass Mathematics Solutions for Exercise - H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Statistics, Exercise 5: EXERCISE

Questions from H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Statistics, Exercise 5: EXERCISE with Hints & Solutions

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