Question

Gender	Age	Ethnicity	Marital	Qualification	PostSchool	Hours	Income
Male	23	European	Never	Vocational	Yes	70	884
Female	42	Other	Married	Vocational	Yes	27	525
Female	22	European	Never	School	No	15	309
Male	40	Maori	Previously	Vocational	Yes	39	517
Female	22	Pacific	Never	School	No	8	86
Female	18	European	Never	School	No	17	255
Male	24	European	Never	Degree	Yes	40	860
Female	32	European	Married	None	No	10	211
Male	35	European	Married	School	No	70	1131
Female	34	European	Other	None	No	25	386
Female	45	European	Married	School	No	16	299
Female	30	Maori	Never	School	No	40	819
Male	35	European	Previously	Degree	Yes	45	934
Female	33	European	Never	Vocational	Yes	8	299
Male	45	European	Married	Degree	Yes	50	1614
Female	39	European	Other	Degree	Yes	55	1152
Male	42	European	Previously	Degree	Yes	54	856
Male	33	European	Previously	Degree	Yes	60	548
Female	43	European	Previously	None	No	25	266

Please help me complete the following tasks with step-by-step explanations:

Create a Frequency (Pivot) Table of the Qualification and Gender variables. Compare the modal Qualification for each Gender.

Draw a suitable graph of the Ethnicity variable, and comment on what it shows

Draw boxplots of Hours Worked by Qualification. Ensure the ordinal nature of Qualification is reflected in the graph. Use your graph to compare the hours worked for the four groups, i.e. explain what the graph shows.

Calculate the mean and standard deviation of the Hours data, and the 90th percentile. What does the latter number describe about the hours worked?

Calculate the mean and standard deviation of the Income variable for males and females separately. (Hint: consider using the Sort functionality) Draw boxplots of the Income variable by Gender. Do the means and standard deviations agree with the information shown by the boxplots? Explain.

Draw a histogram of the Income variable. Summarise the sample distribution.  If the histogram is bimodal, can you explain the source of this?

Answer 1

gender(with qualification)	Count of gender
female	11
degree	1
none	3
school	5
vocational	2
male	8
degree	5
school	1
vocational	2
Grand Total	19

as we can see that modal qualification for female is school whereas for male is degree

it shows that european ethnicity is the most among all the sample data points. It tells us that european are the majority and more in numbers.

The box plot shows us that the central tendancy of degree in basis of hours worked is more than all the other four qualifications whereas the spread or dispersion of vocational is most than the rest of the three. School has the lowest median among the others. This tells us that degree has the most consistent work hours among the peers and also the most work hours.

The mean of hours=total/19=35.47

standard deviation of hours==20.62

for the 90th percentile we sort the hours data by ascending order first

we get

8
8
10
15
16
17
25
25
27
39
40
40
45
50
54
55
60
70
70

90th percentile=90/100 *(N+1) th value of the sorted data= 18th value of the sorted data= 70

The 90th percentile is the value of the hours for which 90% of the data is below/lesser than it

Variable   gender   Mean   StDev
income   female   418.8   309.0
male 918   346

yes the box plots of the male and female incomes agree with the data as we can see that the median(central tendancy) is around the same as shown in the data. Also the spread of the male is higher than the female as shown in the boxplot as the whiskers are more for the male than the female which indicates a higher standard deviation.

income	Count of income
86-235	2
236-385	5
386-535	3
536-685	1
686-835	1
836-985	4
986-1135	1
1136-1285	1
1586-1735	1

we can see that it is a bimodal distribution with two peaks at 236-385 range and 836-985 range

The bimodal might be due to the the presence of two high frequency of two different income groups where the majority of the people lie. It indicates two different groups with local maximum and minumum.