Find the mean, by Direct Method: Class interval 0 - 100 100 - 200 200 - 300 300 - 400 400 - 500 Frequency 6 9 15 12 8

If x 1 , x 2 , x 3 , . . . . . . , x n are the class marks with corresponding frequencies f 1 , f 2 , f 3 , . . . . . . . , f n respectively, then, Mean = x ¯ = f 1 x 1 + f 2 x 2 + f 3 x 3 + . . . . . . . + f n x n f 1 + f 2 + f 3 + . . . . . . . + f n = ∑ f i x i ∑ f i From the given data, we can plot the below table: Class interval Frequency f i Class Mark x i f i x i 0 - 100 6 0 + 100 2 = 100 2 = 50 300 100 - 200 9 150 1350 200 - 300 15 250 3750 300 - 400 12 350 4200 400 - 500 8 450 3600 ∑ f i = 50 ∑ f i x i = 13200 Mean = ( x ¯ ) = Σ f i x i Σ f i = 13200 50 = 264 Hence, the mean is 264 .

Find the mean by Short-cut Method (Assumed Mean method). Class interval 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 Frequency 12 16 6 7 9

From the given data, we can plot the below table: Class interval Frequency f i Class Mark x i Deviations d i = x i - 25 f i d i 0 - 10 12 0 + 10 2 = 10 2 = 5 5 - 25 = - 20 - 240 10 - 20 16 15 - 10 - 160 20 - 30 6 25 = a 0 0 30 - 40 7 35 10 70 40 - 50 9 45 20 180 ∑ f i = 50 ∑ f i d i = - 150 Let a = 25 be the assumed mean, then we have, Mean ( x ¯ ) = a + Σ f i d i Σ f i = 25 + ( - 150 ) 50 = 25 – 3 = 22 Hence, the mean is 22 . Note: Answer mentioned in the book is incorrect the correct answer is: 22 .

Find the mean by Short-cut Method (Assumed Mean method). Class interval 0 - 20 20 - 40 40 - 60 60 - 80 80 - 100 100 - 200 Frequency 20 35 52 44 38 31

From the given data, we can plot the below table: Class interval Frequency f i Class Mark x i Deviations d i = x i - a f i d i 0 - 20 20 0 + 20 2 = 20 2 = 10 10 - 50 = - 40 - 800 20 - 40 35 30 - 20 - 700 40 - 60 52 50 = a 0 0 60 - 80 44 70 20 880 80 - 100 38 90 40 1520 100 - 120 31 110 60 1860 ∑ f i = 220 ∑ f i d i = 2760 Let, a = 50 be the assumed mean, then we have, Mean ( x ¯ ) = a + Σ f i d i Σ f i = 50 + ( 2760 ) 220 = 50 + 12 . 55 = 62 . 55 approx . Hence, the mean is 62 . 55 .

EASY

10th CBSE

IMPORTANT

Earn 100

Find the mean, by Direct Method:

Class interval $25 - 35$ $35 - 55$ $45 - 55$ $55 - 65$ $65 - 75$

Frequency $6$ $10$ $8$ $12$ $4$

Important Questions on Statistics

EASY

10th CBSE

IMPORTANT

Modern's abc+ of Mathematics for Class 10>Chapter 14 - Statistics>EXERCISE>Q 4

Find the mean, by Direct Method:

Class interval	$0 - 100$	$100 - 200$	$200 - 300$	$300 - 400$	$400 - 500$
Frequency	$6$	$9$	$15$	$12$	$8$

MEDIUM

10th CBSE

IMPORTANT

Modern's abc+ of Mathematics for Class 10>Chapter 14 - Statistics>EXERCISE>Q 5

The mean of the following frequency distribution is $24$ . Find the value of $p$ .

Marks	$0 - 10$	$Mean = (\bar{x}) = \frac{Σ f_{i} x_{i}}{Σ f_{i}}$	$20 - 30$	$30 - 40$	$40 - 50$
Number of students	$15$	$20$	$35$	$p$	$10$

MEDIUM

10th CBSE

IMPORTANT

Modern's abc+ of Mathematics for Class 10>Chapter 14 - Statistics>EXERCISE>Q 6

If the mean of the following distribution is $54$ , find the value of $p$ .

Class interval	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$
Frequency	$7$	$p$	$10$	$9$	$13$

MEDIUM

10th CBSE

IMPORTANT

Modern's abc+ of Mathematics for Class 10>Chapter 14 - Statistics>EXERCISE>Q 7

The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is $₹ 18$ . Find the missing frequency $f$ .

Daily pocket allowance (in $₹$ )	$11 - 13$	$13 - 15$	$15 - 17$	$17 - 19$	$19 - 21$	$21 - 23$	$23 - 25$
Frequency	$7$	$6$	$9$	$13$	$f$	$5$	$4$

MEDIUM

10th CBSE

IMPORTANT

Modern's abc+ of Mathematics for Class 10>Chapter 14 - Statistics>EXERCISE>Q 8

The mean of the following frequency distribution is $57.6$ and the sum of the observations is $50$ . Find the missing frequencies $f_{1}$ and $f_{2}$ .

Class interval	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$	$100 - 120$
Frequency	$7$	$f_{1}$	$12$	$f_{2}$	$8$	$5$

MEDIUM

10th CBSE

IMPORTANT

Modern's abc+ of Mathematics for Class 10>Chapter 14 - Statistics>EXERCISE>Q 9

The mean of the following frequency distribution is $62.8$ and the sum of the frequencies is $50$ . Compute the missing frequency $f_{1}$ and $f_{2}$ .

Class interval	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$	$100 - 120$
Frequency	$7$	$f_{1}$	$12$	$f_{2}$	$7$	$8$

MEDIUM

10th CBSE

IMPORTANT

Modern's abc+ of Mathematics for Class 10>Chapter 14 - Statistics>EXERCISE>Q 10

Find the mean by Short-cut Method (Assumed Mean method).

Class interval	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
Frequency	$12$	$16$	$6$	$7$	$9$

MEDIUM

10th CBSE

IMPORTANT

Modern's abc+ of Mathematics for Class 10>Chapter 14 - Statistics>EXERCISE>Q 11

Find the mean by Short-cut Method (Assumed Mean method).

Class interval	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$	$100 - 200$
Frequency	$20$	$35$	$52$	$44$	$38$	$31$

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

Find the mean, by Direct Method: Class interval 25-35 35-55 45-55 55-65 65-75 Frequency 6 10 8 12 4

Important Questions on Statistics

Learn and Prepare for any exam you want !

Find the mean, by Direct Method:

Class interval $25 - 35$ $35 - 55$ $45 - 55$ $55 - 65$ $65 - 75$

Frequency $6$ $10$ $8$ $12$ $4$