A set of raw scores has been provided listing the test scores earned by your Sta

Question

A set of raw scores has been provided listing the test scores earned by your Statistics 001 course at Pierce College for Exam Build a frequency distribution table demonstrating the frequency and the relative frequency for the raw data. Calculate the mean and the standard deviation for the set of raw scores. (Show your work) Calculate your z score and percentile ranking (draw your distribution, identify the z score and shade the percentile ranking on the distribution in a different color) Is your score an extreme score? (If yes, why?) Where does your score fall in reference to the empirical rule? (The middle 68%, 95% or minority of 98%?) What is the probability of randomly selecting an individual from this population who has an exam score... a. Greater than 25? Symbolically, what is p(X > 25)? b. P (x

Explanation / Answer

Frequency distribution, relative frequency, and other realted calculations are given in the table below, after the theory back-up.

Back-up Theory

Let xi = mid-point of the ith class interval. We define di = (xi - midpoint of the middle class)/Class width.

Then, mean of d = dbar = sum(fidi)/sumfi

Standard Deviation of d = SD(d) = {sum(fidi^2)/sumfi} - (dbar)^2

Mean of x = xbar = (dbar x class width) + midpoint of the middle class

i Class Interval Tally Marks Frequency Relative Mid- di = fixdi fixdi^2 dbar = 1.266667 Lower Boundary Upper Boundary (fi) Frequency Point (xi - 19)/3 Var(d = ) 1.862222 (fi/N) (xi) SD(d) = 1.364633 1 8.5 11.5 | 1 0.0333333 10 -3 -3 9 Xbar 22.8 2 11.5 14.5 | 1 0.0333333 13 -2 -2 4 SD(X) = 4.093898 3 14.5 17.5 | 1 0.0333333 16 -1 -1 1 4 17.5 20.5 ||| 3 0.1 19 0 0 0 5 20.5 23.5 ||||| || 7 0.2333333 22 1 7 7 6 23.5 26.5 ||||| ||||| |||| 14 0.4666667 25 2 28 56 7 26.5 29.5 ||| 3 0.1 28 3 9 27 Total 30 1 38 104

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