A set of n = 5 pairs of X and Y values has SX = 10, SY = 20, and SXY = 10. For this set of scores, what is the value of SP?
To find the value of SP, we need to use the formula:
SP = sqrt((n*SX^2 - (SX)^2) * (n*SY^2 - (SY)^2) - (n*SXY - SX*SY)^2) / (n^2 - n)
Let's calculate it step by step:
1. Substitute the given values:
SX = 10
SY = 20
SXY = 10
n = 5
2. Calculate the values inside the square root:
(n * SX^2 - SX^2) = (5 * 10^2 - 10^2) = (5 * 100 - 100) = 400
(n * SY^2 - SY^2) = (5 * 20^2 - 20^2) = (5 * 400 - 400) = 1800
(n * SXY - SX * SY) = (5 * 10 - 10 * 20) = (50 - 200) = -150
3. Calculate the numerator of the final expression:
Numerator = (400 * 1800 - (-150)^2) = (720000 - 22500) = 697500
4. Calculate the denominator of the final expression:
Denominator = (n^2 - n) = (5^2 - 5) = (25 - 5) = 20
5. Calculate the value of SP:
SP = sqrt(Numerator / Denominator) = sqrt(697500 / 20) = sqrt(34875) ≈ 186.96
Therefore, the value of SP for this set of scores is approximately 186.96.