Question

A drug rehabilitation center has kept records of the number of days that their former patients have remained drug free. Compute the range, mean, variance, and the standard deviation.

88	93	65	77	77	106	123	139	142	190
97	143	88

Use this information to answers questions #4 - #6.

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Question 4

What is the sample mean? (round to the thousandths)

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Question 5

What is the standard deviation? (round to the thousandths)

Question 6

Complete the 2x14 table by calculating the z score for each patient.

# of Days	z score
88
93
65
77
77
106
123
139
142
190
97
143
88

Answer 1

S.No		X	(X-x̄)	(X-x̄)2
1		88	-21.846	477.25444
2		93	-16.846	283.79290
3		65	-44.846	2011.17751
4		77	-32.846	1078.86982
5		77	-32.846	1078.86982
6		106	-3.846	14.79290
7		123	13.154	173.02367
8		139	29.154	849.94675
9		142	32.154	1033.86982
10		190	80.154	6424.63905
11		97	-12.846	165.02367
12		143	33.154	1099.17751
13		88	-21.846	477.25444
Σx		1428	Σ(X-x̄)2=	15167.6923
x̄=Σx/n		109.8462	s2=Σ(x-x̄)2/(n-1)=	1263.97436
			s=√s2    =	35.552

Range =max-min =190-65 =125

variance =1263.794

from above

4)

sample mean =109.846

b)

standard deviation =35.552

6)

X			z score=(x-mean)/s
88			-0.61
93			-0.47
65			-1.26
77			-0.92
77			-0.92
106			-0.11
123			0.37
139			0.82
142			0.90
190			2.25
97			-0.36
143			0.93
88			-0.61