Three sample data sets for variable x are given as follow. Data set A: 19, 35, 3
ID: 3131250 • Letter: T
Question
Three sample data sets for variable x are given as follow. Data set A: 19, 35, 35,41,43, 58, 60, 64, 77, 81, 92 Find the mean, mode, standard deviation, 85th percentile, five number summary and interquartile range for Data set A. If Data sets A, B and C are mixed. Find the combined mean and standard deviation. Suppose each data in Data set C is increased by 10%, find the new mean and variance. Suppose we find the corresponding data for variable y is 83532, calculate the sample covariance and correlation for variable x and y. Calculate and comment on the coefficient of determination.Explanation / Answer
a) Ascending Order ... 19 35 35 41 43 58 60 64 77 81 92
Min 19
Q1 35
Median 58
Q2 77
Max 92
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b) Combined sum = 605+513+649 = 1747
Combined n = 31
Hence mean combined = 1767/31 = 57
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Combined sum of X^2 = 32553+503^2 +59^2+461.818+55^2 (Using the formula X^2 = Var +Mean^2)
292529.8
Var(X) =
= 289380.8
Std dev = 537.848
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Variance will not change
But total will be 649(1.1)= 713.9 for C
Combined total = 1767+64.9
Hence combined mean = 1831.9/31 = 59.094
D) Cov (xy) = E(XY)-E(X)E(Y)
83532/31-(1426)(1747)/31^2
=102.2581
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