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Given r=0.8 ,sum of xy =60, sum of xsquare = 90 standard deviation of y = 2.5 find the number of items?
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Given r=0.8 ,sum of xy =60, sum of xsquare = 90 standard deviation of ...
Given Data:
- Correlation coefficient (r) = 0.8
- Sum of xy = 60
- Sum of x^2 = 90
- Standard deviation of y = 2.5
Finding the Number of Items:
Formula for Correlation Coefficient:
r = Σ((x - mean of x)(y - mean of y)) / (√(Σ(x - mean of x)^2) * √(Σ(y - mean of y)^2))
Using the Given Data:
- Σxy = 60
- Σx^2 = 90
- Standard deviation of y = 2.5
Calculating Σ(x - mean of x)^2:
Σ(x - mean of x)^2 = Σx^2 - (Σx)^2 / n
90 = (Σx)^2 / n
Calculating Σ(y - mean of y)^2:
(2.5)^2 = Σ(y - mean of y)^2 / n
Substitute the Values in the Correlation Coefficient Formula:
0.8 = 60 / (√90 * √(2.5)^2)
Solving for n:
- Substitute the values and solve the equation to find the number of items (n).
Explanation:
- The correlation coefficient formula is used to find the relationship between two variables.
- By substituting the given values into the formula, we can solve for the number of items in the dataset.
- Calculating the sum of squares and deviations helps in determining the correlation coefficient accurately.
By following these steps and calculations, you can find the number of items in the dataset based on the given correlation coefficient and other data points.
- Correlation coefficient (r) = 0.8
- Sum of xy = 60
- Sum of x^2 = 90
- Standard deviation of y = 2.5
Finding the Number of Items:
Formula for Correlation Coefficient:
r = Σ((x - mean of x)(y - mean of y)) / (√(Σ(x - mean of x)^2) * √(Σ(y - mean of y)^2))
Using the Given Data:
- Σxy = 60
- Σx^2 = 90
- Standard deviation of y = 2.5
Calculating Σ(x - mean of x)^2:
Σ(x - mean of x)^2 = Σx^2 - (Σx)^2 / n
90 = (Σx)^2 / n
Calculating Σ(y - mean of y)^2:
(2.5)^2 = Σ(y - mean of y)^2 / n
Substitute the Values in the Correlation Coefficient Formula:
0.8 = 60 / (√90 * √(2.5)^2)
Solving for n:
- Substitute the values and solve the equation to find the number of items (n).
Explanation:
- The correlation coefficient formula is used to find the relationship between two variables.
- By substituting the given values into the formula, we can solve for the number of items in the dataset.
- Calculating the sum of squares and deviations helps in determining the correlation coefficient accurately.
By following these steps and calculations, you can find the number of items in the dataset based on the given correlation coefficient and other data points.
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Given r=0.8 ,sum of xy =60, sum of xsquare = 90 standard deviation of y = 2.5 find the number of items?
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Given r=0.8 ,sum of xy =60, sum of xsquare = 90 standard deviation of y = 2.5 find the number of items? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Given r=0.8 ,sum of xy =60, sum of xsquare = 90 standard deviation of y = 2.5 find the number of items? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given r=0.8 ,sum of xy =60, sum of xsquare = 90 standard deviation of y = 2.5 find the number of items?.
Given r=0.8 ,sum of xy =60, sum of xsquare = 90 standard deviation of y = 2.5 find the number of items? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Given r=0.8 ,sum of xy =60, sum of xsquare = 90 standard deviation of y = 2.5 find the number of items? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given r=0.8 ,sum of xy =60, sum of xsquare = 90 standard deviation of y = 2.5 find the number of items?.
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