If the mean of the distribution is 33 . 2 and the sum of all frequencies is 100 , then find the missing frequencies f 1 and f 2 . class 6 - 14 14 - 22 22 - 30 30 - 38 38 - 46 46 - 54 54 - 62 62 - 70 frequency 11 21 f 1 15 14 8 f 2 6

Solution: Given: Let assumed mean be A = 34 Class width = h = 8 The table for the given data: class x i f i u i = x i - A h f i u i 6 - 14 10 11 - 3 - 33 14 - 22 18 21 - 2 - 42 22 - 30 26 f 1 - 1 - f 1 30 - 38 34 = A 15 0 0 38 - 46 42 14 1 14 46 - 54 50 8 2 16 54 - 62 58 f 2 3 3 f 2 62 - 70 66 6 4 24 Total ∑ f i = 75 + f 1 + f 2 ∑ f i u i = 3 f 2 - f 1 - 21 Hence , ∑ f i = 75 + f 1 + f 2 = 100 f 1 + f 2 = 25 . . . . . ( i ) Mean = A + ∑ f i u i ∑ f i × h 33 . 2 = 34 + 3 f 2 - f 1 - 21 100 × 8 - 0 . 8 = 3 f 2 - f 1 - 21 100 × 8 3 f 2 - f 1 - 21 = - 10 3 f 2 - f 1 = 11 . . . . . . ( ii ) ( i ) + ( ii ) gives 4 f 2 = 36 f 2 = 9 Substituting, the value of f 2 in ( i ) , gives f 1 = 16 Hence , f 1 = 16 and f 2 = 9

Jitender Gupta and Divya Malik Solutions for Exercise 1: Topic Exercise

Author:Jitender Gupta & Divya Malik

Jitender Gupta Mathematics Solutions for Exercise - Jitender Gupta and Divya Malik Solutions for Exercise 1: Topic Exercise

Attempt the practice questions from Exercise 1: Topic Exercise with hints and solutions to strengthen your understanding. All In One ICSE Mathematics Class 10 solutions are prepared by Experienced Embibe Experts.

Questions from Jitender Gupta and Divya Malik Solutions for Exercise 1: Topic Exercise with Hints & Solutions

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 1

Find the mean of the following distribution:

Class interval	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
Number of workers	$7$	$10$	$15$	$8$	$10$

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 2

Find the mean of the following data:

Class	$25 - 35$	$35 - 45$	$45 - 55$	$55 - 65$	$65 - 75$
Frequency	$6$	$10$	$8$	$12$	$4$

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 3

The table below shows the daily expenditure on food of $50$ households in a locality.

Daily expenditure (in $₹$ )	$0 - 100$	$100 - 200$	$200 - 300$	$300 - 400$	$400 - 500$
Numbers of workers	$6$	$9$	$15$	$12$	$8$

Find the mean daily expenditure (in $₹$ ) on food.

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 4

If the mean of given data is $50$ , find the value of $p$ .

Class interval	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$
Frequency	$17$	$28$	$32$	$p$	$19$

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 6

Calculate the mean of the following data.

Class	$4 - 7$	$8 - 11$	$12 - 15$	$16 - 19$
Frequency	$5$	$4$	$9$	$10$

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 8

The data on the number of patients attending a hospital in a month is given below

Number of patients	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$
Number of days	$4$	$4$	$7$	$20$	$12$	$8$	$5$

Find the average number of patients attending the hospital by using the assumed mean method upto two decimal places.

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 12

The monthly pocket money of students of a class is given in the following frequency distribution

Pocket money $(in ₹)$	$100 - 125$	$125 - 150$	$150 - 175$	$175 - 200$	$200 - 225$
Number of students	$14$	$8$	$12$	$5$	$11$

Find the mean of pocket money using step deviation method.

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 14

If the mean of the distribution is $33.2$ and the sum of all frequencies is $100$ , then find the missing frequencies $f_{1}$ and $f_{2}$ .

class	$6 - 14$	$14 - 22$	$22 - 30$	$30 - 38$	$38 - 46$	$46 - 54$	$54 - 62$	$62 - 70$
frequency	$11$	$21$	$f_{1}$	$15$	$14$	$8$	$f_{2}$	$6$

Jitender Gupta and Divya Malik Solutions for Exercise 1: Topic Exercise

Jitender Gupta Mathematics Solutions for Exercise - Jitender Gupta and Divya Malik Solutions for Exercise 1: Topic Exercise

Questions from Jitender Gupta and Divya Malik Solutions for Exercise 1: Topic Exercise with Hints & Solutions

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