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?

Question

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

Answer Question

Answer 1

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.

Answer 2

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! :)