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Ris equal to -1 mean of X is equal to 4.5 mean of Y is equal to 5.5 standard deviations and square of X is 5.25 and standard deviations and square of y is 5.25 N is equal to 8 one pair of observation X is 9 and Y is 10 omitted to be included and hence to be included?
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Ris equal to -1 mean of X is equal to 4.5 mean of Y is equal to 5.5 st...
One Pair of Observation Omitted:
Given information:
- r (correlation coefficient) = -1
- Mean of X (µX) = 4.5
- Mean of Y (µY) = 5.5
- Standard deviation of X (σX^2) = 5.25
- Standard deviation of Y (σY^2) = 5.25
- N (number of observations) = 8
To determine whether to include or omit one pair of observations, we need to consider the impact on the correlation coefficient (r).
Step 1: Calculate the Sum of X and Y
- Sum of X (ΣX) = N * µX = 8 * 4.5 = 36
- Sum of Y (ΣY) = N * µY = 8 * 5.5 = 44
Step 2: Calculate the Sum of X^2 and Y^2
- Sum of X^2 (ΣX^2) = N * σX^2 + ΣX^2 = 8 * 5.25 + 36^2 = 42 + 1296 = 1338
- Sum of Y^2 (ΣY^2) = N * σY^2 + ΣY^2 = 8 * 5.25 + 44^2 = 42 + 1936 = 1978
Step 3: Calculate the Cross-Product Sum of XY
- Cross-Product Sum of XY (ΣXY) = N * r * σX * σY + ΣXY = 8 * -1 * √(σX^2 * σY^2) + 36 * 44 = -8 * √(5.25 * 5.25) + 1584 = -8 * 5.25 + 1584 = 1579.5
Step 4: Calculate the Correlation Coefficient
- r = (ΣXY - (ΣX * ΣY) / N) / √((ΣX^2 - (ΣX)^2 / N) * (ΣY^2 - (ΣY)^2 / N))
- r = (1579.5 - (36 * 44) / 8) / √((1338 - (36)^2 / 8) * (1978 - (44)^2 / 8))
- r = (1579.5 - 1584) / √((1338 - 1296 / 8) * (1978 - 1936 / 8))
- r = -4.5 / √((1338 - 1296 / 8) * (1978 - 1936 / 8))
- r = -4.5 / √((1338 - 1296 / 8) * (1978 - 1936 / 8))
- r = -4.5 / √((1338 - 1296 / 8) * (1978 - 1936 / 8))
- r = -4.5 / √((1338 - 1296 / 8) * (1978 -
Given information:
- r (correlation coefficient) = -1
- Mean of X (µX) = 4.5
- Mean of Y (µY) = 5.5
- Standard deviation of X (σX^2) = 5.25
- Standard deviation of Y (σY^2) = 5.25
- N (number of observations) = 8
To determine whether to include or omit one pair of observations, we need to consider the impact on the correlation coefficient (r).
Step 1: Calculate the Sum of X and Y
- Sum of X (ΣX) = N * µX = 8 * 4.5 = 36
- Sum of Y (ΣY) = N * µY = 8 * 5.5 = 44
Step 2: Calculate the Sum of X^2 and Y^2
- Sum of X^2 (ΣX^2) = N * σX^2 + ΣX^2 = 8 * 5.25 + 36^2 = 42 + 1296 = 1338
- Sum of Y^2 (ΣY^2) = N * σY^2 + ΣY^2 = 8 * 5.25 + 44^2 = 42 + 1936 = 1978
Step 3: Calculate the Cross-Product Sum of XY
- Cross-Product Sum of XY (ΣXY) = N * r * σX * σY + ΣXY = 8 * -1 * √(σX^2 * σY^2) + 36 * 44 = -8 * √(5.25 * 5.25) + 1584 = -8 * 5.25 + 1584 = 1579.5
Step 4: Calculate the Correlation Coefficient
- r = (ΣXY - (ΣX * ΣY) / N) / √((ΣX^2 - (ΣX)^2 / N) * (ΣY^2 - (ΣY)^2 / N))
- r = (1579.5 - (36 * 44) / 8) / √((1338 - (36)^2 / 8) * (1978 - (44)^2 / 8))
- r = (1579.5 - 1584) / √((1338 - 1296 / 8) * (1978 - 1936 / 8))
- r = -4.5 / √((1338 - 1296 / 8) * (1978 - 1936 / 8))
- r = -4.5 / √((1338 - 1296 / 8) * (1978 - 1936 / 8))
- r = -4.5 / √((1338 - 1296 / 8) * (1978 - 1936 / 8))
- r = -4.5 / √((1338 - 1296 / 8) * (1978 -
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Ris equal to -1 mean of X is equal to 4.5 mean of Y is equal to 5.5 standard deviations and square of X is 5.25 and standard deviations and square of y is 5.25 N is equal to 8 one pair of observation X is 9 and Y is 10 omitted to be included and hence to be included?
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Ris equal to -1 mean of X is equal to 4.5 mean of Y is equal to 5.5 standard deviations and square of X is 5.25 and standard deviations and square of y is 5.25 N is equal to 8 one pair of observation X is 9 and Y is 10 omitted to be included and hence to be included? 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 Ris equal to -1 mean of X is equal to 4.5 mean of Y is equal to 5.5 standard deviations and square of X is 5.25 and standard deviations and square of y is 5.25 N is equal to 8 one pair of observation X is 9 and Y is 10 omitted to be included and hence to be included? covers all topics & solutions for B Com 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ris equal to -1 mean of X is equal to 4.5 mean of Y is equal to 5.5 standard deviations and square of X is 5.25 and standard deviations and square of y is 5.25 N is equal to 8 one pair of observation X is 9 and Y is 10 omitted to be included and hence to be included?.
Ris equal to -1 mean of X is equal to 4.5 mean of Y is equal to 5.5 standard deviations and square of X is 5.25 and standard deviations and square of y is 5.25 N is equal to 8 one pair of observation X is 9 and Y is 10 omitted to be included and hence to be included? 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 Ris equal to -1 mean of X is equal to 4.5 mean of Y is equal to 5.5 standard deviations and square of X is 5.25 and standard deviations and square of y is 5.25 N is equal to 8 one pair of observation X is 9 and Y is 10 omitted to be included and hence to be included? covers all topics & solutions for B Com 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ris equal to -1 mean of X is equal to 4.5 mean of Y is equal to 5.5 standard deviations and square of X is 5.25 and standard deviations and square of y is 5.25 N is equal to 8 one pair of observation X is 9 and Y is 10 omitted to be included and hence to be included?.
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