The mean and standard deviation of heights and weights of 50 students of a class are as follows: Weights Heights Mean 63 .2 kg 160 cm Standard deviation 5 . 6 kg 29 . 2 cm Which shows more variability, heights or weights ?

For weights , x 1 ¯ = 63 .2 ; σ 1 = 5 .6 So, C . V in weights = σ 1 x 1 ¯ × 100 = 5 .6 63 .2 × 100 = 8 . 8608 For heights = σ 2 x 2 ¯ × 100 = 29 .2 × 100 160 = 18 . 25 Thus, coefficient of variation in heights is greater than C . V in weights . Hence, heights shows more variability.

Share prices ₹ of two companies, X and Y are given below for a 10 - week period. Find whose share is more stable. X 35 54 52 53 56 58 52 50 51 49 Y 108 107 105 105 106 107 104 103 104 101

For company X , number of observations = 10 Sum of all observations = 35 + 54 + 52 + 53 + 56 + 58 + 52 + 50 + 51 + 49 = 510 So, mean = X ¯ = Sum of all observations Number of observations = 510 10 = 51 For company Y , number of observations = 10 Sum of all observations = 108 + 107 + 105 + 105 + 106 + 107 + 104 + 103 + 104 + 101 = 1050 So, mean = Y ¯ = Sum of all observations Number of observations = 1050 10 = 105 The table is as below: X 35 54 52 53 56 58 52 50 51 49 Y 108 107 105 105 106 107 104 103 104 101 X - X ¯ - 16 3 1 2 5 7 1 - 1 0 - 2 X - X ¯ 2 256 9 1 4 25 49 1 1 0 4 Σ ( X − X ¯ ) 2 = 350 Y - Y ¯ 3 2 0 0 1 2 - 1 - 2 - 1 - 4 Y - Y ¯ 2 9 4 0 0 1 4 1 4 1 16 Σ ( Y − Y ¯ ) 2 = 40 σ X = Σ ( X − X ¯ ) 2 n = 350 10 = 35 And, σ Y = Σ ( Y − Y ¯ ) 2 n = 40 10 = 2 So, C . V for series X = σ X X ¯ × 100 = 5 .91608 51 × 100 = 11 .6002 C . V for series Y = σ y Y ¯ × 100 = 2 105 × 100 = 1 .9048 So, C . V for series X is greater than C . V for series Y . Thus series Y is more stable than series X . Hence, series Y is more stable than the share of series X .

Life of bulb produced by two factories A and B are given below: Length of life (in hours ) Factory A (Number of bulbs) Factory B (Number of bulbs) 550 - 650 10 8 650 - 750 22 60 750 - 850 52 24 850 - 950 20 16 950 - 1050 16 12 120 120 The bulbs of which factory are more consistent from the point of view of length of life?

Length of life x i Class mark f A f B d i = x i - A ' A ' = 800 u i = d i C C = 100 f A u i f A u i 2 f B u i f B u i 2 550 - 650 600 10 8 - 200 - 2 - 20 40 - 16 32 650 - 750 700 22 60 - 100 - 1 - 22 22 - 60 60 750 - 850 800 52 24 0 0 0 0 0 0 850 - 950 900 20 16 100 1 20 20 16 16 950 - 1050 1000 16 12 200 2 32 64 24 48 Σ f A = 120 Σ f B = 120 ∑ f A u i = 10 ∑ f A u i 2 = 146 ∑ f B u i = - 36 ∑ f B u i 2 = 156 For factory A , by step deviation method x A ¯ = A ′ + Σ f A u i Σ f A × C = 800 + 10 120 × 100 = 808 .33 σ A = Σ f A u i 2 Σ f A − Σ f A u i Σ f A 2 × C = 146 120 − 10 120 2 × 100 = 1 .2167 − 0 .00694 × 100 = 1 .20976 × 100 = 109 .9891 So, C . V for factory A = σ A x A ¯ × 100 = 109 .9891 × 100 808 .33 = 13 .607 For factory B , by step deviation method x B ¯ = A ′ + Σ f B u i Σ f B × C C = 800 + ( − 36 ) 120 × 100 = 770 and σ B = ∑ f B u i 2 Σ f B − Σ f B u i ∑ f B 2 × C = 156 120 − − 36 120 2 × 100 = 1 . 3 − 0 .09 × 100 = 110 So, C . V for factory B = σ B x B ¯ × 100 = 110 770 × 100 = 14 . 29 Thus, C . V for factory B is more than C . V for factory A . Hence, the bulbs of factory A are more consistent than that of B from the point of view of length of life.

M L Aggarwal Solutions for Chapter: Statistics, Exercise 6: EXERCISE

Author:M L Aggarwal

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Chapter: Statistics, Exercise 6: EXERCISE

Attempt the practice questions on Chapter 14: Statistics, Exercise 6: EXERCISE with hints and solutions to strengthen your understanding. Understanding ISC Mathematics Class 11 Volume 2 solutions are prepared by Experienced Embibe Experts.

Questions from M L Aggarwal Solutions for Chapter: Statistics, Exercise 6: EXERCISE with Hints & Solutions

EASY

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 14 - Statistics>EXERCISE>Q 4

The mean and standard deviation of $heights$ and $weights$ of $50$ students of a class are as follows:

	$Weights$	$Heights$
Mean	$63 .2 kg$	$160 cm$
Standard deviation	$5.6 kg$	$29.2 cm$

Which shows more variability, $heights$ or $weights ?$

EASY

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 14 - Statistics>EXERCISE>Q 5

Coefficients of variation of two distributions are $60$ and $70,$ and their standard deviations are $21$ and $16$ respectively. What are their arithmetic means?

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 14 - Statistics>EXERCISE>Q 6

Find the coefficient of variation for the following data:

Size of item	$10$	$11$	$12$	$13$	$14$	$15$	$16$
Frequency	$2$	$7$	$11$	$15$	$10$	$4$	$1$

(Write your answer up to two decimal places.)

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 14 - Statistics>EXERCISE>Q 7

Calculate the coefficient of variation from the following data:

Income $(₹)$	Number of families
$1000 - 1700$	$12$
$1700 - 2400$	$18$
$2400 - 3100$	$20$
$3100 - 3800$	$25$
$3800 - 4500$	$35$
$4500 - 5200$	$10$

(write the answer up to two decimal places.)

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 14 - Statistics>EXERCISE>Q 8

Find the coefficient of variation for the following data:

Marks	$20 - 29$	$30 - 39$	$40 - 49$	$50 - 59$	$60 - 69$	$70 - 79$	$80 - 89$	$90 - 99$
Number of students	$5$	$12$	$15$	$20$	$18$	$10$	$6$	$4$

(Write the answer upto two decimal places.)

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 14 - Statistics>EXERCISE>Q 9

Find the coefficient of variation for the following data:

Size (in $cm$ )	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$
No. of items	$2$	$8$	$20$	$35$	$20$	$15$

(Write the answer upto two decimal places.)

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 14 - Statistics>EXERCISE>Q 10

Share prices $(₹)$ of two companies, $X$ and $Y$ are given below for a $10 -$ week period. Find whose share is more stable.

$X$	$35$	$54$	$52$	$53$	$56$	$58$	$52$	$50$	$51$	$49$
$Y$	$108$	$107$	$105$	$105$	$106$	$107$	$104$	$103$	$104$	$101$

HARD

11th ICSE

IMPORTANT

Understanding ISC Mathematics Class 11 Volume 2>Chapter 14 - Statistics>EXERCISE>Q 11

Life of bulb produced by two factories $A$ and $B$ are given below:

Length of life (in $hours$ )	Factory $A$ (Number of bulbs)	Factory $B$ (Number of bulbs)
$550 - 650$	$10$	$8$
$650 - 750$	$22$	$60$
$750 - 850$	$52$	$24$
$850 - 950$	$20$	$16$
$950 - 1050$	$16$	$12$
	$120$	$120$

The bulbs of which factory are more consistent from the point of view of length of life?

M L Aggarwal Solutions for Chapter: Statistics, Exercise 6: EXERCISE

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Chapter: Statistics, Exercise 6: EXERCISE

Questions from M L Aggarwal Solutions for Chapter: Statistics, Exercise 6: EXERCISE with Hints & Solutions

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