JNU SSS 2010 Question 43: Descriptive statistics and dispersion
Consider a country in which there are four different types of people Red, Blue, Green and Yellow. All Reds earn the same income. The same is true about the Blues, Greens and Yellows. However the Red income, the Blue income, the Green income and Yellow income can be different from each other. A distribution of income of the country (Di) specifies the Red income, Blue income, Green income and Yellow income and also the number of Reds, Blues, Greens and Yellows. The following table gives the possible income distributions for the country :
Income: Red
Income: Blue
Income: Green
Income: Yellow
Number of Individuals: Red
Number of Individuals: Blue
Number of Individuals: Green
Number of Individuals: Yellow
D1
1
2
3
4
1
1
1
1
D2
3
4
1
2
1
1
1
1
D3
5
10
15
20
1
1
1
1
D4
0·8
1·6
2·4
5·2
1
1
1
1
D5
2·5
2·5
2·5
2·5
1
1
1
1
D6
1
2
3
4
5
5
5
5
Let σi denote the standard deviation for the income distribution i. Which of the following is true?
Tap an option to check your answer.
Answer and worked solution
Checking your account…
Plain-text version
Consider a country in which there are four different types of people Red, Blue, Green and Yellow. All Reds earn the same income. The same is true about the Blues, Greens and Yellows. However the Red income, the Blue income, the Green income and Yellow income can be different from each other. A distribution of income of the country (Dᵢ) specifies the Red income, Blue income, Green income and Yellow income and also the number of Reds, Blues, Greens and Yellows. The following table gives the possible income distributions for the country: | Income: Red | Income: Blue | Income: Green | Income: Yellow | Number of Individuals: Red | Number of Individuals: Blue | Number of Individuals: Green | Number of Individuals: Yellow | D₁ | 1 | 2 | 3 | 4 | 1 | 1 | 1 | 1 | D₂ | 3 | 4 | 1 | 2 | 1 | 1 | 1 | 1 | D₃ | 5 | 10 | 15 | 20 | 1 | 1 | 1 | 1 | D₄ | 0·8 | 1·6 | 2·4 | 5·2 | 1 | 1 | 1 | 1 | D₅ | 2·5 | 2·5 | 2·5 | 2·5 | 1 | 1 | 1 | 1 | D₆ | 1 | 2 | 3 | 4 | 5 | 5 | 5 | 5 | Let σᵢ denote the standard deviation for the income distribution i. Which of the following is true? (A) σ₅ < σ₁ = σ₂ = σ₆ < σ₄ < σ₃ (B) σ₅ < σ₁ = σ₂ = σ₆ < σ₃ < σ₄ (C) σ₅ < σ₁ = σ₂ < σ₆ < σ₄ < σ₃ (D) σ₅ < σ₁ = σ₆ < σ₂ < σ₄ < σ₃
Also written as: Consider a country in which there are four different types of people Red, Blue, Green and Yellow. All Reds earn the same income. The same is true about the Blues, Greens and Yellows. However the Red income, the Blue income, the Green income and Yellow income can be different from each other. A distribution of income of the country (D_i) specifies the Red income, Blue income, Green income and Yellow income and also the number of Reds, Blues, Greens and Yellows. The following table gives the possible income distributions for the country: | Income: Red | Income: Blue | Income: Green | Income: Yellow | Number of Individuals: Red | Number of Individuals: Blue | Number of Individuals: Green | Number of Individuals: Yellow | D_1 | 1 | 2 | 3 | 4 | 1 | 1 | 1 | 1 | D_2 | 3 | 4 | 1 | 2 | 1 | 1 | 1 | 1 | D_3 | 5 | 10 | 15 | 20 | 1 | 1 | 1 | 1 | D_4 | 0·8 | 1·6 | 2·4 | 5·2 | 1 | 1 | 1 | 1 | D_5 | 2·5 | 2·5 | 2·5 | 2·5 | 1 | 1 | 1 | 1 | D_6 | 1 | 2 | 3 | 4 | 5 | 5 | 5 | 5 | Let sigma_i denote the standard deviation for the income distribution i. Which of the following is true?
Descriptive statistics and dispersion has come up 117 times in 6 exams since 2004.
What this question tests
This question is on Measures of dispersion, part of Descriptive statistics and dispersion in Statistics.
How spread out data are: range, variance, standard deviation and relative measures.
TestStop has 39 past-paper questions on this subtopic.
