Using short cut method, find the mean, variance and standard deviation for the data: Class 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 Frequency 5 8 15 16 6

Mean ( x ¯ ) = ∑ f i x i ∑ f i = 1350 50 = 27 Class Frequency ( f i ) Midpoint x i x i f i x i - x ¯ x ¯ = 27 x i - x ¯ 2 f i x i - x ¯ 2 0 - 10 5 5 25 - 22 484 2420 10 - 20 8 15 120 - 12 144 1152 20 - 30 15 25 375 - 2 4 60 30 - 40 16 35 560 8 64 1024 40 - 50 6 45 270 18 324 1944 ∑ f i = 50 ∑ f i x i = 1350 28 ∑ f i x i - x ¯ 2 = 6600 Variance σ 2 = ∑ f i x i - x ¯ 2 ∑ f i = 6600 50 = 132 Standard deviation σ = Variance = 132 = 11 . 49

Using short cut method, find the mean, variance and standard deviation for the data: Class 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 90 - 100 Frequency 3 7 12 15 8 3 2

Mean ( x ¯ ) = ∑ f i x i ∑ f i = 3100 50 = 62 Class Frequency ( f i ) Midpoint x i x i f i x i - x ¯ x ¯ = 62 x i - x ¯ 2 f i x i - x ¯ 2 30 - 40 3 35 105 - 27 729 2187 40 - 50 7 45 315 - 17 289 2023 50 - 60 12 55 660 - 7 49 588 60 - 70 15 65 975 3 9 135 70 - 80 8 75 600 13 169 1352 80 - 90 3 85 255 23 529 1587 90 - 100 2 95 190 33 1089 2178 ∑ f i = 50 ∑ f i x i = 3100 ∑ f i x i - x ¯ 2 = 10050 Variance σ 2 = ∑ f i x i - x ¯ 2 ∑ f i = 10050 50 = 201 Standard deviation σ = Variance = 201 = 14 . 17

Using short cut method, find the mean, variance and standard deviation for the data: Class 25 - 35 35 - 45 45 - 55 55 - 65 65 - 75 Frequency 64 132 153 140 51

Mean ( x ¯ ) = ∑ f i x i ∑ f i = 26820 540 = 49 . 67 Class Frequency ( f i ) Midpoint x i x i f i x i - x ¯ x ¯ = 49 . 67 x i - x ¯ 2 f i x i - x ¯ 2 25 - 35 64 30 1920 - 19 . 67 386 . 9089 24762 . 1696 35 - 45 132 40 5280 - 9 . 67 93 . 5089 12343 . 1748 45 - 55 153 50 7650 0 . 33 0 . 1089 16 . 6617 55 - 65 140 60 8400 10 . 33 106 . 7089 14939 . 246 65 - 75 51 70 3570 20 . 33 413 . 3089 21078 . 7539 ∑ f i = 540 ∑ f i x i = 26820 ∑ f i x i - x ¯ 2 = 73140 . 006 Variance σ 2 = ∑ f i x i - x ¯ 2 ∑ f i = 73140 . 006 540 = 135 . 44 Standard deviation σ = Variance = 135 . 44 = 11 . 64

E M B I B E

Senior Secondary School Mathematics FOR CLASS 11>Statistics and Probability>Chapter 30 - Statistics>EXERCISE

R S Aggarwal Solutions for Exercise 2: EXERCISE

Author:R S Aggarwal

R S Aggarwal Mathematics Solutions for Exercise - R S Aggarwal Solutions for Exercise 2: EXERCISE

Attempt the practice questions from Exercise 2: EXERCISE with hints and solutions to strengthen your understanding. Senior Secondary School Mathematics FOR CLASS 11 solutions are prepared by Experienced Embibe Experts.

Questions from R S Aggarwal Solutions for Exercise 2: EXERCISE with Hints & Solutions

HARD

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 30 - Statistics>EXERCISE>Q 2

Find the mean, variance and standard deviation for first six odd natural numbers.

HARD

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 30 - Statistics>EXERCISE>Q 3

Using short cut method, find the mean, variance and standand deviation for the data:

$x_{i}$	$4$	$8$	$11$	$17$	$20$	$24$	$32$
$f_{i}$	$3$	$5$	$9$	$5$	$4$	$3$	$1$

HARD

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 30 - Statistics>EXERCISE>Q 4

Using short cut method, find the mean, variance and standand deviation for the data:

$x_{i}$	$6$	$10$	$14$	$18$	$24$	$28$	$30$
$f_{i}$	$2$	$4$	$7$	$12$	$8$	$4$	$3$

HARD

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 30 - Statistics>EXERCISE>Q 5

Using short cut method, find the mean, variance and standand deviation for the data:

$x_{i}$	$10$	$15$	$18$	$20$	$25$
$f_{i}$	$3$	$2$	$5$	$8$	$2$

HARD

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 30 - Statistics>EXERCISE>Q 6

Using short cut method, find the mean, variance and standand deviation for the data:

$x_{i}$	$92$	$93$	$97$	$98$	$102$	$104$	$109$
$f_{i}$	$3$	$2$	$3$	$2$	$6$	$3$	$3$

HARD

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 30 - Statistics>EXERCISE>Q 7

Using short cut method, find the mean, variance and standard deviation for the data:

$\begin{matrix} Class & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 \\ Frequency & 5 & 8 & 15 & 16 & 6 \end{matrix}$

HARD

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 30 - Statistics>EXERCISE>Q 8

Using short cut method, find the mean, variance and standard deviation for the data:

$\begin{matrix} Class & 30 - 40 & 40 - 50 & 50 - 60 & 60 - 70 & 70 - 80 & 80 - 90 & 90 - 100 \\ Frequency & 3 & 7 & 12 & 15 & 8 & 3 & 2 \end{matrix}$

HARD

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 30 - Statistics>EXERCISE>Q 9

Using short cut method, find the mean, variance and standard deviation for the data:

$\begin{matrix} Class & 25 - 35 & 35 - 45 & 45 - 55 & 55 - 65 & 65 - 75 \\ Frequency & 64 & 132 & 153 & 140 & 51 \end{matrix}$

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