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Chapters
2: Collection of Data
3: Organisation of Data
4: Presentation of Data
5: Measures of Central Tendency
▶ 6: Measures of Dispersion
7: Correlation
8: Index Numbers
Chapter 9: Use of Statistical Tools
![NCERT solutions for Statistics for Economics [English] chapter 6 - Measures of Dispersion - Shaalaa.com](/images/statistics-for-economics-english_6:098eda7804764399818daa37556a8f8c.jpg "NCERT solutions for Statistics for Economics [English] chapter 6 - Measures of Dispersion")
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Solutions for Chapter 6: Measures of Dispersion
Below listed, you can find solutions for Chapter 6 of CBSE NCERT for Statistics for Economics [English].
NCERT solutions for Statistics for Economics [English] 6 Measures of Dispersion Exercise [Pages 89 - 90]
A measure of dispersion is a good supplement to the central value in understanding a frequency distribution. Comment.
Which measure of dispersion is the best and how?
Some measures of dispersion depend upon the spread of values whereas some are estimated on the basis of the variation of values from a central value. Do you agree?
In a town, 25% of the persons earned more than Rs 45,000 whereas 75% earned more than 18,000. Calculate the absolute and relative values of dispersion.
The yield of wheat and rice per acre for 10 districts of a state is as under:
|
District |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
| Wheat |
12 |
10 |
15 |
19 |
21 |
16 |
18 |
9 |
25 |
10 |
| Rice |
22 |
29 |
12 |
23 |
18 |
15 |
12 |
34 |
18 |
12 |
Calculate for each crop,
Range
The yield of wheat and rice per acre for 10 districts of a state is as under:
|
District |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
| Wheat |
12 |
10 |
15 |
19 |
21 |
16 |
18 |
9 |
25 |
10 |
| Rice |
22 |
29 |
12 |
23 |
18 |
15 |
12 |
34 |
18 |
12 |
Calculate for each crop,
Q.D.
The yield of wheat and rice per acre for 10 districts of a state is as under:
|
District |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
| Wheat |
12 |
10 |
15 |
19 |
21 |
16 |
18 |
9 |
25 |
10 |
| Rice |
22 |
29 |
12 |
23 |
18 |
15 |
12 |
34 |
18 |
12 |
Calculate for each crop,
Mean deviation about Mean
The yield of wheat and rice per acre for 10 districts of a state is as under:
|
District |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
| Wheat |
12 |
10 |
15 |
19 |
21 |
16 |
18 |
9 |
25 |
10 |
| Rice |
22 |
29 |
12 |
23 |
18 |
15 |
12 |
34 |
18 |
12 |
Calculate for each crop,
Mean deviation about Median
The yield of wheat and rice per acre for 10 districts of a state is as under:
|
District |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
| Wheat |
12 |
10 |
15 |
19 |
21 |
16 |
18 |
9 |
25 |
10 |
| Rice |
22 |
29 |
12 |
23 |
18 |
15 |
12 |
34 |
18 |
12 |
Calculate for each crop,
Standard deviation
The yield of wheat and rice per acre for 10 districts of a state is as under:
|
District |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
| Wheat |
12 |
10 |
15 |
19 |
21 |
16 |
18 |
9 |
25 |
10 |
| Rice |
22 |
29 |
12 |
23 |
18 |
15 |
12 |
34 |
18 |
12 |
Calculate for each crop,
Which crop has greater variation?
The yield of wheat and rice per acre for 10 districts of a state is as under:
|
District |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
| Wheat |
12 |
10 |
15 |
19 |
21 |
16 |
18 |
9 |
25 |
10 |
| Rice |
22 |
29 |
12 |
23 |
18 |
15 |
12 |
34 |
18 |
12 |
Calculate for each crop,
Compare the values of different measures for each crop.
In the previous question, calculate the relative measures of variation and indicate the value which, in your opinion, is more reliable.
A batsman is to be selected for a cricket team. The choice is between X and Y on the basis of their scores in five previous tests which are:
| X |
25 |
85 |
40 |
80 |
120 |
| Y |
50 |
70 |
65 |
45 |
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 |
|
Which brand gives higher life?
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 |
|
Which brand is more dependable?
The 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 are the new average daily wage and standard deviation? Have the wages become more or less uniform?
If in the previous question, each worker is given a hike of 10 % in wages, how are the mean and standard deviation values affected?
Calculate the mean deviation using 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 |
The sum of 10 values is 100 and the sum of their squares is 1090. Find out the coefficient of variation.
Solutions for 6: Measures of Dispersion
NCERT solutions for Statistics for Economics [English] chapter 6 - Measures of Dispersion
Shaalaa.com has the CBSE Mathematics Statistics for Economics [English] CBSE solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. NCERT solutions for Mathematics Statistics for Economics [English] CBSE 6 (Measures of Dispersion) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.
Further, we at Shaalaa.com provide such solutions so students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.
Concepts covered in Statistics for Economics [English] chapter 6 Measures of Dispersion are Lorenz Curve, Measures of Central Tendency - Mean, Measures of Central Tendency - Median, Measures of Central Tendency - Mode, Measures of Central Tendency - Central Value Or Representative Value, Measures of Central Tendency - Series, Measures of Central Tendency - Partition Value, Measures of Central Tendency - Quartile, Measures of Central Tendency - Deciles, Measures of Central Tendency - Percentile, Measures of Dispersion - Absolute Dispersion, Measures of Dispersion - Relative Dispersion, Lorenz Curve, Correlation Meaning, Properties of Correlation,, Types of Correlation, Scatter Diagram of Correlation, Measures of Correlation - Karl Pearson'S Method (Two Variables Ungrouped Data), Measures of Correlation - Spearman's Rank Correlation, Meaning of Index Numbers, Uses of Index Numbers, Types of Index Number - Wholesale Price Index, Types of Index Number - Consumer Price Index, Types of Index Number - Index of Industrial Production, Construction of Price Index, Cost of Living Index Number, Inflation and Index Numbers, Method to Measure - Simple Aggregate Method, Method to Measure - Simple Average Price Relative Method, Method to Measure - Laspeyer Method, Method to Measure - Paasche's Index Numer, Method to Measure - Fisher's Method, Introduction to Measures of Dispersion, Measures Based Upon Spread of Values, Measures of Dispersion from Average, Absolute and Relative Measures of Dispersion, Lorenz Curve, Measures of Dispersion - Conclusion.
Using NCERT Statistics for Economics [English] solutions Measures of Dispersion exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in NCERT Solutions are essential questions that can be asked in the final exam. Maximum CBSE Statistics for Economics [English] students prefer NCERT Textbook Solutions to score more in exams.
Get the free view of Chapter 6, Measures of Dispersion Statistics for Economics [English] additional questions for Mathematics Statistics for Economics [English] CBSE, and you can use Shaalaa.com to keep it handy for your exam preparation.
