Question

Compute the mean and standard deviation for the following sample of n = 4 scores: 82, 88, 82, 86 (Hint: To simplify the arithmetic, you can subtract 80 points from each score to obtain a new sample consisting of 2, 8, 2, and 6.) Compute the mean and standard deviation for the new sample. Mean: Standard deviation: What are the values of the mean and standard deviation for the original sample? Mean: Standard deviation:

Answer 1

Answer:- The Known Sample is 82,88,82, 86 let the Sample Size ben=4) The formula for the Sample mean is n MEXI 0 Find the Sample mean substitude the known value is Eqno M. 82+88+82 +86 4 322 -84.5 338 84.5 Therefore, the sample mean for the original data is M = 84.5 The formula for the standard deviation is ECX-M)2 5- M)* — n -1

Find the sample standard deviation substitute the known values is Eq"0 E CX-64:5)? 4-1 (82-84.5)+(88.-84-931(82-84.55 + (86.84,5)2 Therefore, the sample standad deviation for the original datais 15=3] The transformed data is 2,8,2 and 6 > Find the sample mean substitute the known values in Eq" O 2+8+2+6 M= aroma m=4.5

Therefore, the sample mean for the transformed data is M:4:5 Find the stondard deviation substitute the known values in Eqn {(X-4.5)2 4 -1 (2-4,5)768-4,5)2+(2-4.5)+(6-4.5)? = 3 Therefore, the sample standard deviation for the transformed data is S=3