Question

Question 1 A psychiatrist studying student depression asked 30 students of MTH177 how many times a day they wished they did not have to take statistics. She recorded the following data: 3, 5, 1, 0, 6, 8, 8, 5, 2, 3, 2, 0, 7, 6, 7, 4, 2, 15, 25, 3, 1, 1, 4, 3, 5, 6, 7, 8, 1, 2, 3, 5 Sorted: (0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 15, 25)

A) She has asked you to organize the data into table showing frequency, relative frequency, and cumulative frequency.

B) She has also asked you for a relative frequency bar chart (Remember to label)

C) She has also asked for the calculation of:

a. the mean and standard deviation (of the ungrouped data),

b. the median and the five number summary with a box-and-whisker diagram,

c. the mode

d. with regard to the outlier problem, she has asked for the calculation of a 10% trimmed mean, and also for the calculation of outliers using the inter quartile range method.

Answer 1

Problem has an anomaly: It mentions 30 students, but data given is of 30 students. Following solution is as per given data, and not the mentioned 30 students

A)

X	Frequency (f)	Rel. Frequency	Cululative Frequency
0	2	0.0625	2
1	4	0.125	6
2	4	0.125	10
3	5	0.15625	15
4	2	0.0625	17
5	4	0.125	21
6	3	0.09375	24
7	3	0.09375	27
8	3	0.09375	30
15	1	0.03125	31
25	1	0.03125	32
TOTAL →	32	1

B)

C)

a,

X	Frequency (f)	X*f	X^2*f
0	2	0	0
1	4	4	4
2	4	8	16
3	5	15	45
4	2	8	32
5	4	20	100
6	3	18	108
7	3	21	147
8	3	24	192
15	1	15	225
25	1	25	625
TOTAL →	32	158	1494

b.

Thus boxplot can be drawn with these values

c.

Mode = 3 (Highest frequency, 5)

d.

For trimmed mean, we are given α = 0.1, when n = 32

k = nα = 3.2, n-2k = 25.6

So trim 3 observations from either end, and consider only 8-% of the first term from either end

Thus 0, 0, 1, 8, 15, 25 get trimmed and take ony 80% of 1 and 8, the next observations

Outliers: IQR = Q3 - Q1 = 4.75

Lower bound = Q1 - 1.5 IQR which is less than zero, so not to be considered

Upper bound = Q3 + 1.5 IQR = 13.875, so outliers are 15, 25

Note again: Values may need to be chaged depending on whether problem wants us tot ake 30 values (in which case I was not sure which 2 values to not take). The above steps are correct, please take into account how data is given

Excel Link: https://drive.google.com/file/d/13zpWwLKVRp06rtWzOxkDvGajRQh9yysS/view?usp=sharing