JNU SSS 2010 Question 44: 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 μi denote the median for the income distribution i. Which of the following is true?
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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 μᵢ denote the median for the income distribution i. Which of the following is true? (A) μ₄ < μ₁ = μ₂ = μ₅ < μ₆ < μ₃ (B) μ₄ < μ₁ = μ₂ = μ₅ = μ₆ < μ₃ (C) The mean is equal to the median for each of the given distributions (D) The mean is different from the median for each of the given distributions
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 mu_i denote the median 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 Median, mode and quantiles, part of Descriptive statistics and dispersion in Statistics.
Positional averages and how to locate them in raw and grouped data.
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