Question

Below is the summary information for sites operated by waste management companies in Arkansas. The number of these Superfund sites in each of the 75 counties in Arkansas is shown in the table.

3	2	1	2	0	5	3	5	2	1	8	2
3	5	3	1	3	0	8	0	9	6	8	6
16	0	6	0	5	5	0	1	25	0	0	0
2	10	12	3	10	3	17	2	4	2	1	21
2	1	11	5	2	2	7	2	3	1	8	2
0	0	2	3	10	2	3	48	21

a. How many Superfund sites are there in Arkansas?

b. 50% of the counties have at least how many sites?

c. Is this data skewed? If so, identify the type of skew and justify your answer.

d. Based upon your analysis, is the mean representative of this data set? If not, what is the source of the problem? Be specific.

e. If there was a problem in part (d) correct it and re-calculate the mean.

f. What does the variance equal in this setting?

g. For the Superfund sites data, create the appropriate box plot:

For the boxplot, what is the: (3 pts each)

a. median =                                                   b. largest value =

c. smallest value =                                       d. first quartile =

e. third quartile =

Answer 1

Excel Addon Megastat used for calculations:

Below is the summary information for sites operated by waste management companies in Arkansas. The number of these Superfund sites in each of the 75 counties in Arkansas is shown in the table.

3	2	1	2	0	5	3	5	2	1	8	2
3	5	3	1	3	0	8	0	9	6	8	6
16	0	6	0	5	5	0	1	25	0	0	0
2	10	12	3	10	3	17	2	4	2	1	21
2	1	11	5	2	2	7	2	3	1	8	2
0	0	2	3	10	2	3	48	21

a. How many Superfund sites are there in Arkansas?

Sample size=69

b. 50% of the counties have at least how many sites?

Median=3, 50% of the counties have at least 3 sites.

c. Is this data skewed? If so, identify the type of skew and justify your answer.

Mean= 5.30, median =3

Mean > median, therefore data is positively skewed.

d. Based upon your analysis, is the mean representative of this data set? If not, what is the source of the problem? Be specific.

Since data is positively skewed, mean is not representative of this data set.

There are some large outliers in the data set.

e. If there was a problem in part (d) correct it and re-calculate the mean.

There are 4 extreme values in the data set, 21,21,25 and 48

After removing these values, new mean = 3.86

Descriptive statistics
count	65
mean	3.8615
sample standard deviation	3.8604
sample variance	14.9024

f. What does the variance equal in this setting?

The new variance = 14.9024

g. For the Superfund sites data, create the appropriate box plot:

For the boxplot, what is the: (3 pts each)

a. median =    3                                               b. largest value =48

c. smallest value =   0                                    d. first quartile =1

e. third quartile =6

Descriptive statistics
count	69
mean	5.3043
sample standard deviation	7.4682
sample variance	55.7737
minimum	0
maximum	48
range	48
1st quartile	1.00
median	3.00
3rd quartile	6.00
interquartile range	5.00
mode	2.00