Question

1.

The following table gives a sample of the percentage of current users of alcohol and cigarettes in the 18- to 25-year-old age group in the United States for some recent selected years. Find the average, sample variance, and sample standard deviation of each. (Round your answers to four decimal places.)

Alcohol	77	69	73	76	66	78
Cigarettes	24	18	22	29	21	26

Alcohol:

mean
sample variance
sample standard deviation

Cigarettes:

mean
sample variance
sample standard deviation

Which group of users is varying more?

cigarettes

alcohol    

cannot be determined

2.

If the random variable X denotes the real valued outcomes given in the following table with the given frequency of occurrence of each of the outcomes, fill in the last line of the table and find the expected value of X.

Outcome	-2	-1	0	1	2
Frequency	26	26	10	20	12
P(X)

E(X) =  

Answer 1

For Alcohol group explanation for sample variance :

data	data-mean	(data - mean)2
77	3.8333	14.69418889
69	-4.1667	17.36138889
73	-0.1667	0.02778889
76	2.8333	8.02758889
66	-7.1667	51.36158889
78	4.8333	23.36078889

Find the sum of numbers in the last column to get.

∑(xi−X bar )²=114.8333

For cigarettes group explanation for sample variance :

data	data-mean	(data - mean)2
24	0.6667	0.44448889
18	-5.3333	28.44408889
22	-1.3333	1.77768889
29	5.6667	32.11148889
21	-2.3333	5.44428889
26	2.6667	7.11128889

Find the sum of numbers in the last column to get.

∑(xi−X bar )²=75.3333