Question

A marketing researcher asked 70 adults how many times they went out to a movie in the last month. Find the standard deviation for the survey responses summarized in the table below:

x	0	1	2	3	4	5	8	10	12	15	20
f	12	16	12	10	12	2	1	1	2	1	1

The following data are the price of gas at 15 gas stations (in $/gallon):     

2.46 2.49 2.54 2.59 2.60 2.75 2.75 2.76   2.78   2.79 2.79 2.79 2.81 2.92 3.06

              (a) Find the mean and standard deviation for the given data.

              (b) What proportion of the data lies within:

                     * one standard deviation of the mean

                     * two standard deviations of the mean

                     * three standard deviations of the mean?

Answer 1

1)

X	f	X*f	(X-X_bar)^2	(X-X_bar)^2*f
0	12	0	8.576530612	102.9183673
1	16	16	1	16
2	12	24	4	48
3	10	30	9	90
4	12	48	16	192
5	2	10	25	50
8	1	8	64	64
10	1	10	100	100
12	2	24	144	288
15	1	15	225	225
20	1	20	400	400
Sum	70	205	Sum	1575.918367
Mean	2.9285714

Mean=

Standard deviation:

2)a) Mean=

Standard deviation:

b) One standard deviation of the mean:

: 10/15 =0.66667

two standard deviations of the mean:

: 14/15 =0.9333

three standard deviations of the mean:

: 15/15 =1