Question

We are interested in studying the performance of college students on statistics exams. In any
given semester, there are hundreds of students taking statistics in the department of psychology,
mathematics, business, or other related departments that offer a course on statistics. We
randomly select 20 students from the roster of all students enrolled in statistics for the spring
semester and administer questionnaires throughout the semester, as well as collect their
assignment and exam grades. In our first analysis, we are interested in examining the grades
from all the students on Exam 1 in their course. All exams were out of 100 points. This data is
below:

90 75 67 56 89 88 34 67 95 81 76 69 72 73 79 83 42 53 78 80

1. Draw a frequency distribution of the data. What can you determine from this
distribution?
2. What is your dependent variable and what scale of measurement is this variable?
pt.
3. We collected data from 20 students. Would you consider these students to be a
sample or population? Explain your answer in 1-2 sentences.
4. Is it important to have a normal distribution here? Why or why not?
5. Is this data skewed? Explain your answer?
6. Calculate the mean, median, and mode for this data.
7. Calculate the variance and standard deviation for this data using the table below.
Show all of your work.

Answer 1

3. We collected data from 20 students. Would you consider these students to be a
sample or population? Explain your answer in 1-2 sentences.

it is sample and sample size is n=20

we have taken sample of 20 students randomly from population of all students enrolled in statistics for the spring
semester

Solution6

6. Calculate the mean, median, and mode for this data.

mean=sum/total=1447/20=72.35

median is middlemost value after sorting the numbers

34 42 53 56 67 69 72 73 75 76 78 79 80 81 83 88 89 90 95

median is middlemost value after sorting

median=75+76/2=75.5

mode is middlemost value .it is 67

67 repeats 2 times

7. Calculate the variance and standard deviation for this data using the table below.

X	X - mean	(X-mean)2	X2
90	17.65	311.5225	8100
75	2.65	7.0225	5625
67	-5.35	28.6225	4489
56	-16.35	267.3225	3136
89	16.65	277.2225	7921
88	15.65	244.9225	7744
34	-38.35	1470.7225	1156
67	-5.35	28.6225	4489
95	22.65	513.0225	9025
81	8.65	74.8225	6561
76	3.65	13.3225	5776
69	-3.35	11.2225	4761
72	-0.35	0.1225	5184
73	0.65	0.4225	5329
79	6.65	44.2225	6241
83	10.65	113.4225	6889
42	-30.35	921.1225	1764
53	-19.35	374.4225	2809
78	5.65	31.9225	6084
80	7.65	58.5225	6400
1447	1.14E-13	4792.55	109483

variance=4792.55/20-1

=4792.55/19

=  252.2395

variance=252.2395

standard deviation=sqrt(variance)

=sqrt(252.2395)

= 15.88205

standard deviation=15.88205