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.)

25	16	49	40
27	39	38	43
23	41	22	35
46	50	52	42

(a) the 16 students constitute a population

SS
variance
standard deviation

(b) the 16 students constitute a sample

SS
variance
standard deviation

Answer 1

	X	X-Xbar	(X-Xbar)^2
	25	-11.75	138.0625
	16	-20.75	430.5625
	49	12.25	150.0625
	40	3.25	10.5625
	27	-9.75	95.0625
	39	2.25	5.0625
	38	1.25	1.5625
	43	6.25	39.0625
	23	-13.75	189.0625
	41	4.25	18.0625
	22	-14.75	217.5625
	35	-1.75	3.0625
	46	9.25	85.5625
	50	13.25	175.5625
	52	15.25	232.5625
	42	5.25	27.5625
SUM	588		1819
Xbar	36.75	SUM(X)/n
a) Population
SS	1819	SUM(X-Xbar)^2
σ^2	113.69	SS/n	Variance
σ	10.66		Standard deviation
b) Sample
SS	1819	SUM(X-Xbar)^2
S^2	121.27	SS/(n-1)	Variance
S	11.01		Standard deviation