Question

A professor records the time (in minutes) that it takes 16 students to complete an exam. Compute the SS, the variance, and the standard deviation assuming the 16 students constitute a population and assuming the 16 students constitute a sample. (Round your answers for variance and standard deviation to two decimal places.) 38 22 49 32 37 47 36 31 44 19 43 13 20 24 39 46

(a) the 16 students constitute a population

SS

variance standard

(b) the 16 students constitute a sample

SS

Variance

Standard deviation

Answer 1

Ans:

	xi	(xi-33.75)^2
1	38	18.0625
2	22	138.0625
3	49	232.5625
4	32	3.0625
5	37	10.5625
6	47	175.5625
7	36	5.0625
8	31	7.5625
9	44	105.0625
10	19	217.5625
11	43	85.5625
12	13	430.5625
13	20	189.0625
14	24	95.0625
15	39	27.5625
16	46	150.0625
Total	540	1891
mean	33.75

a)SS=1891

Population Variance=1891/16=118.19

Population standard deviation=sqrt(1891/16)=10.87

b)

SS=1891

Sample Variance=1891/(16-1)=126.07

Sample standard deviation=sqrt(1891/(6-1))=11.23