the following set of data is from a sample of n equals 6. 2,9,7,2,10,13 Compute the mean, median, and mode. Compute the range, variance, standard deviation, and coefficient of variation.Compute the Z scores?


2 Answers

Lia Tan Profile
Lia Tan , Statistics Major, answered

Mean = (6+2+9+7+2+10+13)/7 = 49/7 = 7

Median: 1) first put the data in ascending order

2, 2, 6, 7, 9, 10, 13

2) Median is the number in the middle = 7

Mode: What appears most in the sample = 2

Range: Min to max = 2 to 13

Variance of sample: Sum((x-mean)^2)/(n-1) = 16.666667

Standard Deviation = sqrt(variance) = sqrt(16.666667) = 4.082483

Coefficient of Variance (CV): Standard deviation/mean = 0.583212

Unbiased Coefficient of Variance: (1 + 1/4n) * CV = 0.604041

Z-scores: (x - mean)/standard deviation

2: Z = (2 - 7)/4.082483 = -1.22474

6: Z= -0.24495

7: Z = 0

9: Z = 0.489898

10: Z = 0.734847

13: Z = 1.469694

Honestly, you could've just Googled how to do all of these. You can easily compute this using simple tools like a calculator or Microsoft Excel. But anyway, here are your answers.

3 People thanked the writer.
Joe Hyppolite
Joe Hyppolite commented
wait why would add the 6 since the simple size is 6 as in n=6
Lia Tan
Lia Tan commented
Ah I think I misread the question and thought 6 was also in the data set. Okay if that's the case, then take out the six and redo the calculations. Sorry about that!
Joe Hyppolite
Joe Hyppolite commented
thanks but what about this one if you don't mind
Suppose the rate of return for a particular stock during the past two years was 5% and negative 30 %.
Compute the geometric mean rate of return.
James Laughlin Profile
James Laughlin answered

Agreed, one could have googled this. Nonetheless, for those interested in understanding as opposed to simply getting the steps, here is a related 101-level reading of the z-score formula. Wikipedia is also a good resource for this. Just follow the hyperlinks/citations as necessary; it mostly gives you a nice trail! :)

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