+91-8076753736 support@wiredfaculty.com
logo
logo

Sponsor Area

Measures Of Dispersion

Question
CBSEENST11024380
Wired Faculty App

Calculate the arithmetic mean and standard deviation of the following values:

(i) without grouping

(ii) grouping the value in classes 140–145, 145–150 .............

(iii) grouping them in classes 140–150, 150–160 ............

140

143

143

146

146

146

154

156

159

162

164

174

166

166

167

167

168

168

169

169

169

171

175

175

176

176

178

180

182

182

182

182

182

183

184

186

188

190

190

191

191

192

195

202

217

Solution

(i) Without grouping

X

d

d2

140

–35

1225

143

–32

1024

143

–32

1024

146

–29

841

146

–29

841

146

–29

841

154

–21

441

156

–19

361

159

–16

256

162

–13

169

164

–11

121

164

–11

121

166

–9

81

166

–9

81

167

–8

64

167

–8

64

168

–7

49

168

–7

49

169

–6

36

169

–6

36

169

–6

36

171

–4

16

175

0

0

175

0

0

176

1

1

176

1

1

178

3

9

180

5

25

182

7

49

182

7

49

182

7

49

182

7

49

182

7

49

183

8

64

184

9

81

186

11

121

188

13

169

190

15

225

190

15

225

191

16

256

191

16

256

192

17

289

195

20

400

202

27

729

227

52

2704
   

13577

(ii) Grouping the values in classes 140-145,145-150

(iii) Grouping them in classes 140–150, 150–160.

Classes

Tally

Frequency

M

d'

fd'

d

fd'2

140–150

6

145

–4

–24

16

96

150–160

3

155

–3

–9

9

27

160–170

12

165

–2

–24

4

48

170–180

6

175

–1

–6

1

6

180–190

10

185

0

0

0

0

190-200

6

195

1

6

1

6

200-210

1

205

2

2

4

4

210–220

0

215

3

0

9

0

220–230

1

225

4

4

16

16
   

Σf = 45

    

Σfd'=–51

  

Σfd' = 203

Some More Questions From Measures of Dispersion Chapter

Which measure of dispersion is the best and how?

Some measures of dispersion depend upon the spread of values whereas some calculate the variation of values from a central value. Do you agree?

In a town 25% of the persons earned more than Rs. 45000, whereas 75% earned more than Rs. 18000. Calculate the absolute and relative values of dispersion.

A batsman is to be selected for a cricket team. The choice is between X and Y on the basis of their five previous scores which are:

X

Y

25

50

85

70

40

65

80

45

120

80

Which batsman should be selected if we want

(i) a higher run getter, or

(ii) a more reliable batsman in the team?

To check the quality of two brands of lightbulbs, their life in burning hours was estimated as under for 100 bulbs of each brand.

Life (in hrs)

No. of bulbs

Brand A

Brand B

0–50

15

2

50–100

20

8

100–150

18

60

150–200

25

25

200–250

22

5
 

100

100

(i) Which brand gives higher life?

(ii) Which brand is more dependable?

Average daily wage of 50 workers of a factory was Rs. 200 with a standard deviation of Rs. 40. Each worker is given a raise of Rs. 20. What is the new average daily wage and standard deviation? Have the wages become more or less uniform?

In the previous question, calculate the relative measures of variation and indicate the value, which in your opinion is more reliable.

If in the previous question, each worker is given a hike of 10% in wages, how are the mean and standard deviation values affected?

The sum of 10 values is 100 and the sum of their squares is 1090. Find the coefficient of variation.

Calculate the mean deviation about mean and standard deviation for the following distribution:

Classes

Frequencies

20–40

3

40–80

6

80–100

20

100–120

12

120–140

9
 

50

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation