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

HARD

10th ICSE

IMPORTANT

Earn 100

Find the mean of the following frequency distribution by the assumed mean method.

Class $25 - 30$ $30 - 35$ $35 - 40$ $40 - 45$ $45 - 50$ $50 - 55$ $55 - 60$

Frequency $14$ $22$ $16$ $6$ $5$ $3$ $4$

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Important Questions on Statistics

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 9

Using the assumed mean method, find the mean of the following frequency distribution.

Class	$63 - 65$	$66 - 68$	$69 - 71$	$72 - 74$	$75 - 77$
Frequency	$4$	$3$	$7$	$8$	$3$

HARD

10th ICSE

IMPORTANT

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

Find the mean of the following distribution by step-deviation method.

class interval	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
frequency	$10$	$6$	$8$	$12$	$5$	$9$

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 20 - Statistics>Topic Exercise>Q 11

Find the mean of the following data by using step-deviation method.

class	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$
frequency	$17$	$28$	$32$	$24$	$19$

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 13

Calculate the mean of the scores of $20$ students in a Mathematics test.

Marks	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$
Number of students	$2$	$4$	$7$	$6$	$1$

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	$11$	$21$	$f_{1}$	$15$	$14$	$8$	$f_{2}$	$6$

EASY

10th ICSE

IMPORTANT

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

The median of the observations

11

12

14

(x - 2)

(x + 4)

(x + 9)

32

38

and

47

arranged in ascending order is

24

. Find the value of

x

and hence flnd the mean.

Class	$25 - 30$	$30 - 35$	$35 - 40$	$40 - 45$	$45 - 50$	$50 - 55$	$55 - 60$
Frequency	$14$	$22$	$16$	$6$	$5$	$3$	$4$

Find the mean of the following frequency distribution by the assumed mean method. Class 25-30 30-35 35-40 40-45 45-50 50-55 55-60 Frequency 14 22 16 6 5 3 4

Important Questions on Statistics

Learn and Prepare for any exam you want !

Find the mean of the following frequency distribution by the assumed mean method.

Class $25 - 30$ $30 - 35$ $35 - 40$ $40 - 45$ $45 - 50$ $50 - 55$ $55 - 60$

Frequency $14$ $22$ $16$ $6$ $5$ $3$ $4$