Question

A) Determine the sample mean and sample standard deviation.

B) Determine the 5-number summary and the IQR of the following data set. Determine also the outlier/s and the adjacent value/s if relevant.

30,31,41,23,45,30,37,31,37,26,37,24,42,38

Answer 1

a)

Mean = (30 + 31 + 41 + 23 + 45 + 30 + 37 + 31 + 37 + 26 + 37 + 24 + 42 + 38)/14
= 472/14
Mean = 33.7143

Standard Deviation σ = √(1/14 - 1) x ((30 - 33.7143)² + (31 - 33.7143)² + (41 - 33.7143)² + (23 - 33.7143)² + (45 - 33.7143)² + (30 - 33.7143)² + (37 - 33.7143)² + (31 - 33.7143)² + (37 - 33.7143)² + (26 - 33.7143)² + (37 - 33.7143)² + (24 - 33.7143)² + (42 - 33.7143)² + (38 - 33.7143)²)
= √(1/13) x ((-3.7143)² + (-2.7143)² + (7.2857)² + (-10.7143)² + (11.2857)² + (-3.7143)² + (3.2857)² + (-2.7143)² + (3.2857)² + (-7.7143)² + (3.2857)² + (-9.7143)² + (8.2857)² + (4.2857)²)
= √(0.0769) x ((13.79602449) + (7.36742449) + (53.08142449) + (114.79622449) + (127.36702449) + (13.79602449) + (10.79582449) + (7.36742449) + (10.79582449) + (59.51042449) + (10.79582449) + (94.36762449) + (68.65282449) + (18.36722449))
= √(0.0769) x (610.85714286)
= √(46.974914285934)
= 6.8549

b)