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For 10 pairs of observations r = 0.5 The means of x and y are 12 and 15 respectively and their standard deviations are 3 and 4 respectively. While calculating one pair (15,13) was wrongly taken as (16,18). Find the correct value of correlation coefficient.?
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For 10 pairs of observations r = 0.5 The means of x and y are 12 and 1...
Calculation of Correlation Coefficient
Given:
- Number of pairs of observations, n = 10
- Correlation coefficient, r = 0.5
- Mean of x, μx = 12
- Mean of y, μy = 15
- Standard deviation of x, σx = 3
- Standard deviation of y, σy = 4
- Wrongly taken pair, (15,13) as (16,18)
Calculation:
- The formula for correlation coefficient is:
r = Σ((x - μx)(y - μy)) / (nσxσy)
- Using the given values, we can calculate the correlation coefficient as:
r = (10((15-12)(18-15)) + (15-12)(13-15) - (16-12)(18-15) - (16-12)(13-15)) / (10(3)(4))
r = 0.48
Explanation:
- Correlation coefficient is a measure of the strength and direction of the linear relationship between two variables.
- In this case, we are given the value of correlation coefficient, means and standard deviations of x and y, and the number of pairs of observations.
- Using these values, we can calculate the correlation coefficient using the formula mentioned above.
- However, there is an error in one of the pairs of observations, which needs to be corrected.
- We know that the correlation coefficient is highly sensitive to outliers, and even a slight change in the data can affect its value significantly.
- Therefore, we need to correct the wrongly taken pair to get an accurate value of the correlation coefficient.
- Once we have corrected the data, we can apply the formula to calculate the correlation coefficient.
Given:
- Number of pairs of observations, n = 10
- Correlation coefficient, r = 0.5
- Mean of x, μx = 12
- Mean of y, μy = 15
- Standard deviation of x, σx = 3
- Standard deviation of y, σy = 4
- Wrongly taken pair, (15,13) as (16,18)
Calculation:
- The formula for correlation coefficient is:
r = Σ((x - μx)(y - μy)) / (nσxσy)
- Using the given values, we can calculate the correlation coefficient as:
r = (10((15-12)(18-15)) + (15-12)(13-15) - (16-12)(18-15) - (16-12)(13-15)) / (10(3)(4))
r = 0.48
Explanation:
- Correlation coefficient is a measure of the strength and direction of the linear relationship between two variables.
- In this case, we are given the value of correlation coefficient, means and standard deviations of x and y, and the number of pairs of observations.
- Using these values, we can calculate the correlation coefficient using the formula mentioned above.
- However, there is an error in one of the pairs of observations, which needs to be corrected.
- We know that the correlation coefficient is highly sensitive to outliers, and even a slight change in the data can affect its value significantly.
- Therefore, we need to correct the wrongly taken pair to get an accurate value of the correlation coefficient.
- Once we have corrected the data, we can apply the formula to calculate the correlation coefficient.
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For 10 pairs of observations r = 0.5 The means of x and y are 12 and 1...
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For 10 pairs of observations r = 0.5 The means of x and y are 12 and 15 respectively and their standard deviations are 3 and 4 respectively. While calculating one pair (15,13) was wrongly taken as (16,18). Find the correct value of correlation coefficient.?
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For 10 pairs of observations r = 0.5 The means of x and y are 12 and 15 respectively and their standard deviations are 3 and 4 respectively. While calculating one pair (15,13) was wrongly taken as (16,18). Find the correct value of correlation coefficient.? for B Com 2024 is part of B Com preparation. The Question and answers have been prepared according to the B Com exam syllabus. Information about For 10 pairs of observations r = 0.5 The means of x and y are 12 and 15 respectively and their standard deviations are 3 and 4 respectively. While calculating one pair (15,13) was wrongly taken as (16,18). Find the correct value of correlation coefficient.? covers all topics & solutions for B Com 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For 10 pairs of observations r = 0.5 The means of x and y are 12 and 15 respectively and their standard deviations are 3 and 4 respectively. While calculating one pair (15,13) was wrongly taken as (16,18). Find the correct value of correlation coefficient.?.
For 10 pairs of observations r = 0.5 The means of x and y are 12 and 15 respectively and their standard deviations are 3 and 4 respectively. While calculating one pair (15,13) was wrongly taken as (16,18). Find the correct value of correlation coefficient.? for B Com 2024 is part of B Com preparation. The Question and answers have been prepared according to the B Com exam syllabus. Information about For 10 pairs of observations r = 0.5 The means of x and y are 12 and 15 respectively and their standard deviations are 3 and 4 respectively. While calculating one pair (15,13) was wrongly taken as (16,18). Find the correct value of correlation coefficient.? covers all topics & solutions for B Com 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For 10 pairs of observations r = 0.5 The means of x and y are 12 and 15 respectively and their standard deviations are 3 and 4 respectively. While calculating one pair (15,13) was wrongly taken as (16,18). Find the correct value of correlation coefficient.?.
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