Question

Pls answer all three parts for UPVOTE

Data set:

Students Outside US

Stu ID	Age	GPA	Hrs spend on sch wrk
3	48	4.00	7
6	47	2.79	14
9	45	3.48	5
12	19	4.00	30
15	24	3.10	10
18	34	3.24	2
21	44	36.00	6
24	19	2.85	7
27	19	2.80	10
30	27	3.40	8
33	28	2.90	16
36	27	3.40	8
39	28	2.90	16
42	21	2.9	4
45	20	2.50	6
48	23	3.3	18
51	41	3.80	7
54	21	2.60	26
57	39		5
60	18	3.10	12
63	28	3.70	20
66	35		8
69	37	2.80	6
72	21	N/A	21
75	20	3.00	4
78	30	3.50	6
81	21	3.1	4
84	21	3.20	3
87	37	2.86	3
90	19	3.30	12

Students in US:

Stu ID	Age	GPA	Hrs spend on sch wrk
175	20	3.20	10
178	20	2.40	12
181	17	3.98	6
184	20	3.00	15
187	27	2.20	6
190	19	3.00	7
193		3.10	15
196	20		6
199	43	3.67	12
202	44	3.80	10
205	26	3.80	4
208	25	2.50	5
211	21	3.72	10
214	29	2.54	4
217	33	3.85	21
220	18	3.00	5
223	21	3.00	6
226	19	3.00	5
229	26	3.00	4
232	19	2.81	4
235	19	3.00	6
238	28	3.50	10
241	19	4.00	12
244	20	3.20	2
247	21		9
250	20	2.51	3
253	20	3.20	5
256	23		2
259	20	3.10	27
262	26	2.50	8

a) Construct a 5-number summary and boxplot using the variable “hours spent on school work at home” for both groups.

b) Compare the means for both groups to answer the research questions in the first paragraph. Which group has a higher mean GPA? Which group spends more time on their homework? What conclusions can you draw about students who were born in the USA and those who were born outside the USA based on this analysis?

c) Identify any outliers in both groups

Answer 1

a. For students who were born in the USA

The minimum is the smallest value in a data set.

Ordering the data from least to greatest, we get:

2   3   3   4   4   4   5   5   6   6   6   6   7   7   7   8   8   8   10   10   12   12   14   16   16   18   20   21   26   30   

So, the minimum is 2.

The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

2   3   3   4   4   4   5   5   6   6   6   6   7   7   7   8   8   8   10   10   12   12   14   16   16   18   20   21   26   30   

So, the bottom half is

2   3   3   4   4   4   5   5   6   6   6   6   7   7   7   

The median of these numbers is 5.

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

2   3   3   4   4   4   5   5   6   6   6   6   7   7   7   8   8   8   10   10   12   12   14   16   16   18   20   21   26   30   

As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:

Median=

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

2   3   3   4   4   4   5   5   6   6   6   6   7   7   7   8   8   8   10   10   12   12   14   16   16   18   20   21   26   30   

So, the upper half is

8   8   8   10   10   12   12   14   16   16   18   20   21   26   30   

The median of these numbers is 14.

The maximum is the greatest value in a data set.

Ordering the data from least to greatest, we get:

2   3   3   4   4   4   5   5   6   6   6   6   7   7   7   8   8   8   10   10   12   12   14   16   16   18   20   21   26   30   

So, the maximum is 30.

For students born outside the USA

The minimum is the smallest value in a data set.

Ordering the data from least to greatest, we get:

2   2   3   4   4   4   4   5   5   5   5   6   6   6   6   6   7   8   9   10   10   10   10   12   12   12   15   15   21   27   

So, the minimum is 2.

The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

2   2   3   4   4   4   4   5   5   5   5   6   6   6   6   6   7   8   9   10   10   10   10   12   12   12   15   15   21   27   

So, the bottom half is

2   2   3   4   4   4   4   5   5   5   5   6   6   6   6   

The median of these numbers is 5.

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

2   2   3   4   4   4   4   5   5   5   5   6   6   6   6   6   7   8   9   10   10   10   10   12   12   12   15   15   21   27   

As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:

Median=

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

2   2   3   4   4   4   4   5   5   5   5   6   6   6   6   6   7   8   9   10   10   10   10   12   12   12   15   15   21   27   

So, the upper half is

6   7   8   9   10   10   10   10   12   12   12   15   15   21   27   

The median of these numbers is 10.

The maximum is the greatest value in a data set.

Ordering the data from least to greatest, we get:

2   2   3   4   4   4   4   5   5   5   5   6   6   6   6   6   7   8   9   10   10   10   10   12   12   12   15   15   21   27   

So, the maximum is 27

b. For USA students

For non USA students

Mean=

Students of US group have higher mean

US students group spend more time on their homework

We conclude that students who are born in US spend more time on their homework

c. An outlier is defined as being any point of data that lies over 1.5 IQRs below the first quartile (Q1) or above the third quartile (Q3)in a data set.
High = (Q3) + 1.5 IQR
Low = (Q1) – 1.5 IQR

For US group High=14+1.5(14-5)=27.5

For Low=5-1.5(9)=8.5

Hence 30 is outlier for US students

For non US students

High = (Q3) + 1.5 IQR=10+1.5(10-5)=17.5

Low = (Q1) – 1.5 IQR=5-1.5*5=2.5

So 21, 27 are outliers