(a)

The numerical descriptive statistics and histogram chart for incomes in Boise are listed as followed:

Boise

Inter-quartile Range

21100

Mean

16357.35779

Standard Error

422.032757

Median

13000

Mode

0

Standard Deviation

18826.63484

Sample Variance

354442179.4

Kurtosis

53.46858119

Skewness

4.697357512

Range

316500

Minimum

-8800

Maximum

307700

Sum

32551142

Count

1990

Largest(1)

307700

Smallest(1)

-8800

Confidence Level (95.0%)

827.6726617

And the numerical descriptive statistics and histogram chart for incomes in Des Moines are listed as followed:

Des Moines Inter-quartile Range 24225

Mean

21469.37466

Standard Error

521.8665481

Median

20000

Mode

0

Standard Deviation

19885.78627

Sample Variance

395444495.7

Kurtosis

37.58095891

Skewness

3.590159814

Range

325000

Minimum

-10000

Maximum

315000

Sum

31173532

Count

1452

Largest(1)

315000

Smallest(1)

-10000

Confidence Level (95.0%)

1023.69355

The reason that I chose the histogram to present my data is that it always presents ‘continuous data’ which means the data represents measured quantity and we can take the value in a certain range. However the bar chart is usually to present the numbers into the different categories and the pie chart is to present the each of the individual percentage in the total. In this question, the firm wants to know each of the city’s female income level distribution, so the histogram is more suitable.

(b)

From the descriptive statistics, we can see that the average income between the 18 and 40 years old in Des Moines (mean around $21469) is more than the Boise (mean around $16357), so does the median income level ($20000 compared to $13000) And the mode income level for both cities is zero. However, Des Moines’s standard deviation is also bigger than the Boise one which means that the Boise had the high variation from the average mean, so that it is more risky as based on the confidence level at 95%, opening the shop will lose more money in Des Moines than the Boise because of the market risks (around $1023 versus around $827).

For Boise, it has a long tail to the right as it has a positive skewness (positive distribution). Moreover, it has a higher value of kurtosis, thus it has a narrow peak and fat tails respectively. And its peak range from $1 to $20000.

Similar to Boise, Des Moines also has a long tail to the right because of the skewness (positive distribution). However, it has a lower kurtosis value, thus it has a rounded peak and thinner tails respectively. The rounded peaks are from $1 to $30000.

(c)

Except for mean,…