Calculate mean deviation about mean for the following data: Age in years 1 - 5 6 - 10 11 - 15 16 - 20 21 - 25 26 - 30 31 - 35 36 - 40 41 - 45 Number of persons 7 10 16 32 24 18 10 5 1

Given data can be represented as: Age in years Mid value( x i ) Frequency ( f i ) Cumulative Frequency f i x i Deviation D i = x i - x f i D i 0 . 5 - 5 . 5 3 7 7 21 17 . 36 121 . 52 5 . 5 - 10 . 5 8 10 17 80 12 . 36 123 . 6 10 . 5 - 15 . 5 13 16 33 208 7 . 36 117 . 76 15 . 5 - 20 . 5 18 32 65 576 2 . 36 75 . 52 20 . 5 - 25 . 5 23 24 89 552 2 . 64 63 . 36 25 . 5 - 30 . 5 28 18 107 504 7 . 64 137 . 52 30 . 5 - 35 . 5 33 10 117 330 12 . 64 126 . 4 35 . 5 - 40 . 5 38 5 122 190 17 . 64 88 . 2 40 . 5 - 45 . 5 43 1 123 43 22 . 64 22 . 64 ∑ f i = N = 123 ∑ f i x i = 2504 ∑ D i = 102 . 64 ∑ f i D i = x = ∑ f i x i N = 2504 123 = 20 . 36 Mean deviation = ∑ f i D i N = 876 . 52 123 = 7 . 12 .

Following data represents the life of two models of refrigerators A and B . Life(Number of years) 0 - 2 2 - 4 4 - 6 6 - 8 8 - 10 10 - 12 Refrigerator Model A 5 16 13 7 5 4 Model B 2 7 12 19 9 1 Find the mean life of each model. Which model has greater uniformity? Also obtain mode for both models.

Life(No.of years) Model A Frequency( f i ) Cumulative frequency Mid value( x i ) f i × x i d i = x i - x A f i d i 2 0 - 2 5 5 1 5 4 . 12 84 . 872 2 - 4 16 21 3 48 2 . 12 71 . 9104 4 - 6 13 34 5 65 0 . 12 0 . 1872 6 - 8 7 41 7 49 1 . 88 24 . 7408 8 - 10 5 46 9 45 3 . 88 75 . 272 10 - 12 4 50 11 44 5 . 88 138 . 2976 Total N = 50 ∑ f i x i = 256 ∑ f i d i 2 = 395 . 28 x A = ∑ f i x i N = 256 50 = 5 . 12 Standard deviation σ A = ∑ f i d i 2 N = 395 . 28 50 = 2 . 81 Life(No.of years) Model B Frequency( f i ) Cumulative frequency Mid value( x i ) f i × x i d i = x i - x B f i d i 2 0 - 2 2 2 1 2 5 . 16 53 . 2512 2 - 4 7 9 3 21 3 . 16 69 . 8992 4 - 6 12 21 5 60 1 . 16 16 . 1472 6 - 8 19 40 7 133 0 . 84 13 . 4064 8 - 10 9 49 9 81 2 . 84 72 . 5904 10 - 12 1 50 11 11 4 . 84 23 . 4256 Total N = 50 ∑ f i x i = 308 ∑ f i d i 2 = 248 . 72 x B = ∑ f i x i N = 308 50 = 6 . 16 Standard deviation σ B = ∑ f i d i 2 N = 248 . 72 50 = 2 . 23 Coefficient of variation for Model A refrigerators C . V = σ A x A × 100 = 2 . 81 5 . 12 × 100 = 54 . 88 Coefficient of variation for Model B refrigerators C . V = σ B x B × 100 = 2 . 23 6 . 16 × 100 = 36 . 20 The C . V for Model B is less, it indicates that Model B is less variable, more stable, more uniform, more consistent Life(No.of years) Model A frequency Model B frequency 0 - 2 5 2 2 - 4 16 7 4 - 6 13 12 6 - 8 7 19 8 - 10 5 9 10 - 12 4 1 Mode is given by the formula Mode = l + f 1 - f 0 2 f 1 - f 0 - f 2 × C For Model A , Model class is 2 - 4 l = 2 , f 1 = 16 , f 0 = 5 , f 2 = 13 , C = 2 Mode = 2 + 16 - 5 2 × 16 - 5 - 13 × 2 = 3 . 57 Therefore, Model Life of Model A refrigerator is = 3 . 57 y e a r s For Model B , Model class is 6 - 8 l = 6 , f 1 = 19 , f 0 = 12 , f 2 = 9 , C = 2 Mode = 6 + 19 - 12 2 × 19 - 12 - 9 × 2 = 6 . 82 Therefore, Model Life of Model B refrigerator is = 6 . 82 y e a r s

MEDIUM

11th Tamil Nadu Board

IMPORTANT

Earn 100

Distinguish between absolute and relative measures of variation. Give a broad classification of the measures of variations.

Important Questions on Measures of Dispersion

MEDIUM

11th Tamil Nadu Board

IMPORTANT

Statistics Standard 11>Chapter 6 - Measures of Dispersion>EXERCISE>Q 26

Explain and illustrate how the measure of variation afford a supplement to averages in the frequency distribution.

MEDIUM

11th Tamil Nadu Board

IMPORTANT

Statistics Standard 11>Chapter 6 - Measures of Dispersion>EXERCISE>Q 27

What do you understand by 'coefficient of variation?' Discuss its importance in business problems.

HARD

11th Tamil Nadu Board

IMPORTANT

Statistics Standard 11>Chapter 6 - Measures of Dispersion>EXERCISE>Q 28

When is the variance equal to the standard deviation? Under what circumstances can variance be less than the standard deviation? Explain.

HARD

11th Tamil Nadu Board

IMPORTANT

Statistics Standard 11>Chapter 6 - Measures of Dispersion>EXERCISE>Q 29

A retailer uses two different formulas for predicting monthly sales. The first formula has an average of $700$ records, and a standard deviation of $35$ records. The second formula has an average of $300$ records, and a standard deviation of $16$ records. Which formula is relatively less accurate?

MEDIUM

11th Tamil Nadu Board

IMPORTANT

Statistics Standard 11>Chapter 6 - Measures of Dispersion>EXERCISE>Q 30

In a small business firm, two typists are employed typist $A$ and $B$ . Typist $A$ types out, on an average, $30$ pages per day with a standard deviation of $6$ . Typist $B$ , on an average, types out $45$ pages with a standard deviation of $10$ . Which typist shows greater consistency in his output?

MEDIUM

11th Tamil Nadu Board

IMPORTANT

Statistics Standard 11>Chapter 6 - Measures of Dispersion>EXERCISE>Q 31

Calculate mean deviation about mean for the following data:

Age in years	$1 - 5$	$6 - 10$	$11 - 15$	$16 - 20$	$21 - 25$	$26 - 30$	$31 - 35$	$36 - 40$	$41 - 45$
Number of persons	$7$	$10$	$16$	$32$	$24$	$18$	$10$	$5$	$1$

HARD

11th Tamil Nadu Board

IMPORTANT

Statistics Standard 11>Chapter 6 - Measures of Dispersion>EXERCISE>Q 33

Following data represents the life of two models of refrigerators

A

and

B

Life(Number of years)		$0 - 2$	$2 - 4$	$4 - 6$	$6 - 8$	$8 - 10$	$10 - 12$
Refrigerator	Model $A$	$5$	$16$	$13$	$7$	$5$	$4$
Refrigerator	Model $B$	$2$	$7$	$12$	$19$	$9$	$1$

Find the mean life of each model. Which model has greater uniformity? Also obtain mode for both models.

HARD

11th Tamil Nadu Board

IMPORTANT

Statistics Standard 11>Chapter 6 - Measures of Dispersion>EXERCISE>Q 34

Calculate the quartile deviation and coefficient of the quartile deviation from the following data:

Size	$06$	$09$	$12$	$15$	$18$
Frequency	$7$	$12$	$19$	$10$	$2$

Distinguish between absolute and relative measures of variation. Give a broad classification of the measures of variations.

Important Questions on Measures of Dispersion

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