Find the mean, median, 1^st and 3^rd quartile, and standard deviation (round sta

Question

Find the mean, median, 1^st and 3^rd quartile, and standard deviation (round standard deviation to the nearest whole number) for the following SAMPLE set of test scores: 70 72 73 87 84 67 60 55 Mean ________ Median __________ Q1 ____________ Q3 _____ Standard Deviation _______ Using the above information and the Empirical Rule: a. What percent of scores would you expect to fall between 49 and 82? __________ b. 68% of the time you would expect scores between what two values? __________ c. Determine the z-score for a test score of 60. ____________ d. What data value would have a z-score of +3? ________

Explanation / Answer

Ans:

Sorted Data Set: 87, 84, 73, 72, 70, 67, 60, 55

First quartile,Q1=63.5

Third quartile,Q3=78.5

standard deviation=11

a)z score for 49

z=(49-71)/11=-2

z score for 82

z=(82-71)/11=1

P(-2.17<z<1.08)=0.8413-0.02275=0.8185

81.85% will fall between 49 and 82

b)68% of the data lie between one standard deviation from mean

71+11=82

71-11=60

i.e 68% data lie between 60 and 82.

c)z=(60-71)/11=-11/11=-1

d)3=(x-71)/11

33=x-71

x=71+33=104

x=104

Mean: 71 Median: 71 Range: 32 Mode: All values appeared just once. Largest: 87 Smallest: 55 Sum: 568 Count: 8

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