Question

3,9,15, 6,17, 16,32,24,12, 30, 35,12,26,21,25 Using StatKey or other technology, find the following values for the above data Click here to access StatKey (a) The mean and the standard deviation Round your answers to one decimal place. mean standard deviation (b) The five number summary. Enter exact answers. The five number summary is

Answer 1

a)

Mean: $\mu =\sum X_i/n= 283/15=18.86667$

X	Mean	(X-Mean)^2
3	18.86667	251.7511
9	18.86667	97.35111
15	18.86667	14.95111
6	18.86667	165.5511
17	18.86667	3.484444
16	18.86667	8.217778
32	18.86667	172.4844
24	18.86667	26.35111
12	18.86667	47.15111
30	18.86667	123.9511
35	18.86667	260.2844
12	18.86667	47.15111
26	18.86667	50.88444
21	18.86667	4.551111
25	18.86667	37.61778
	Sum	1311.733

Standard deviation: $\sigma =\sqrt{\frac{\sum (X_i-\mu )^2}{n}}=\sqrt{1311.733/15}=9.35141$

b)Five number summary:

Minimum: 3

Q1: (n+1)/4 th observation= (15+1)/4 =4th observation= 12 (Incremental order)

Median: (n+1)/2 th observation= (15+1)/2= 8th observation= 17

Q3:3*(n+1)/4 th observation= 3*(15+1)/4 =3*4=12 th observation= 26

Maximum: 35