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Homework-Ch-03-key

# Homework-Ch-03-key - Chapter 3 Homework key[Over 50 points...

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1 Chapter 3 Homework key 08/30/11 [Over 50 points] 303. [Ch. 3; calc; 14 points] (Descriptive statistics) Given the following data set (12 entries) which represents a SAMPLE: 72 45 65 86 48 77 65 54 86 46 90 86 a. [4 p.] Calculate the range and the IQR. First sort the data from the smallest to the largest value: 45 46 48 54 65 65 72 77 86 86 86 90 Then: X MAX = 90 and X MIN = 45 The range R = 90 - 45 = 45 To find the IQR, we first need to compute the two quartiles: Q 1 = the 25 th %ile: (1) i = 12*0.25 = 3 (2) Since this is a whole number, we average: (3) Q 1 = ½ * (X 3 + X 4 ) = ½ * (48 + 54) = 51 Q 3 = the 75 th %ile: (1) i = 12*0.75 = 9 (2) Since this is a whole number, we average: (3) Q 3 = ½ * (X 9 + X 10 ) = ½ * (86 + 86) = 86.0 Then: IQR = Q 3 Q 1 = 86 51 = 35 b. [6 p.] Calculate the mean, the median, and the mode. The mean = 68.33 The median = Q 2 = ½ * (X 6 + X 7 ) = 68.5 The mode = 86

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2 c. [4 p.] Calculate the variance and standard deviation. First calculate the mean: 820 68.33 12 i x x n Then the variance: 2 2 ( ) 3178.6668 288.9697 1 11 i x x s n And the standard deviation: 2 288.9697 16.9991 s s

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