Statistics problem A sample (data set) contains the observations 13 12 15 10 9 1

Question

Statistics problem

A sample (data set) contains the observations 13 12 15 10 9 11 15 10: find (a) the sample size? (b) sigma_i=1^8 x_i (c) sigma_i=1^8 x_i^2 (d) sigma_i=1^8 (x_i - 10) (e) sigma_i=1^8 (x_i - 10)^2 (f) (sigma_i=1^8 x_i)^2 (g) the sample mean x? (h) the sample variance s^2? (i) the sample standard deviation? (j) the sample median? (k) Is there s (sample) mode? If yes, what is (are) the mode(s)? Recall that s^2 = sigma_i=1^n (x_i - x)^2/n - 1 = sigma_i=1^n x_i^2 - (sigma_i=1^n x_i)^2/n - 1

Explanation / Answer

8 Sample sum = 95 13^2+12^2+……..+10^2 =1165 3+2+5+0-1+1+5+0 =15 65 Part b) squared = 95^2 = 9025 95/8 =11.875 5.267 (5.267)^1/2 = 2.29 (11+12)/2 = 11.5 There are 2 modes (10 and 15)

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