Question

In: Statistics and Probability

Science Majors The Science Department of a a American university collected data on the grade point...

Science Majors The Science Department of a a American university collected data on the grade point average (GPA) of its science majors at the end of their first year of study to investigate their academic performance. The dataset of 224 observations is contained in the file: GPA (THA 1).xlsx. Based on the data, answer the following questions.

Using the Pivot Table in Excel, construct a frequency distribution table of GPA and a histogram displaying the table. Suggested class intervals: 1 – 2, 2 – 3, etc.

Remarks: GPA is a continuous variable. In the Pivot Table output for continuous data, the class (for example) 1 – 2 represents an interval from 1 up to < 2 (i.e. not including 2), and similarly 2 – 3 represents an interval from 2 up to < 3. Do you know which class a GPA of 2 falls into - first or second class? Also don’t forget to remove the gaps between bars.

marks)

Using Excel, compute the sample mean () and sample standard deviation (s). No working is required. (Round your answers to 3 significant figures.)

marks)

Applying the common sense method locate the Q1, Q2 and Q3 of the test scores. Show your working. (Remember to sort the data first.)

Important note: We would like you to practise your understanding of quartiles in this question. If you use Excel or other applications to obtain the answers, you will not get any mark for this question.

By comparing Q2 and the sample mean comment on the skewness of the data. Explain your answer briefly.

An observation is a suspected outlier if it is more than 1.5 times the inter-quartile range (1.5 ´ IQR) below Q1 or above Q3. Use this rule to locate any outliers in the dataset. Show your working.

Remark: (Q1 –1.5 ´ IQR) & (Q3 + 1.5 ´ IQR) are known as the lower and upper fences respectively.

Student ID	GPA
1	6.75
2	3.78
3	4.11
4	3.64
5	5.91
6	5.75
7	5.35
8	1.99
9	4.81
10	4.09
11	5.39
12	5.84
13	1.59
14	2.50
15	4.09
16	6.52
17	6.65
18	7.00
19	3.50
20	5.25
21	4.06
22	4.58
23	5.37
24	5.18
25	6.56
26	5.46
27	3.93
28	5.30
29	1.35
30	5.60
31	2.45
32	4.60
33	3.36
34	5.12
35	6.54
36	4.95
37	5.42
38	4.20
39	4.88
40	3.37
41	3.79
42	3.13
43	5.86
44	6.31
45	4.81
46	6.26
47	4.83
48	6.42
49	6.66
50	5.53
51	5.53
52	6.33
53	3.93
54	4.46
55	4.93
56	5.68
57	3.71
58	3.29
59	4.63
60	3.22
61	3.86
62	5.18
63	4.23
64	5.96
65	5.81
66	4.74
67	5.95
68	4.34
69	4.34
70	1.00
71	5.56
72	5.95
73	5.61
74	4.72
75	5.35
76	7.00
77	6.12
78	4.91
79	3.16
80	6.47
81	5.04
82	4.62
83	5.40
84	4.93
85	5.19
86	4.91
87	5.81
88	5.61
89	6.47
90	5.35
91	5.02
92	3.71
93	3.95
94	3.55
95	4.25
96	4.37
97	2.90
98	5.96
99	3.41
100	5.82
101	2.78
102	4.30
103	6.02
104	2.95
105	1.30
106	4.88
107	1.00
108	3.57
109	3.50
110	2.34
111	4.02
112	5.70
113	5.49
114	3.93
115	1.75
116	4.86
117	3.95
118	3.69
119	4.95
120	1.00
121	4.37
122	4.77
123	4.27
124	1.94
125	5.46
126	3.79
127	3.50
128	3.18
129	5.63
130	5.39
131	1.40
132	4.51
133	3.76
134	4.37
135	3.23
136	1.87
137	5.16
138	6.51
139	1.21
140	4.67
141	4.39
142	2.55
143	4.18
144	5.25
145	5.86
146	4.27
147	5.86
148	6.65
149	4.56
150	4.90
151	5.74
152	5.02
153	5.53
154	5.37
155	6.44
156	5.84
157	6.05
158	4.25
159	4.84
160	6.40
161	3.25
162	3.41
163	5.35
164	3.39
165	5.49
166	4.98
167	6.07
168	5.93
169	6.82
170	6.38
171	6.37
172	4.83
173	5.00
174	4.39
175	5.00
176	5.84
177	5.82
178	6.45
179	3.15
180	4.49
181	3.99
182	3.50
183	4.42
184	2.95
185	5.35
186	4.81
187	4.58
188	3.74
189	3.37
190	5.00
191	4.14
192	2.18
193	5.56
194	5.77
195	4.00
196	4.74
197	4.53
198	5.93
199	4.28
200	4.53
201	4.51
202	4.70
203	4.42
204	5.25
205	3.62
206	3.23
207	5.84
208	4.76
209	7.00
210	5.95
211	5.12
212	3.83
213	5.81
214	5.96
215	3.15
216	2.66
217	4.16
218	3.65
219	5.65
220	2.31
221	4.06
222	1.48
223	2.80
224	3.99

Expert Solution

a)

b)

mean 4.60375 AVERAGE(B2:B225)
sd 1.331621032 STDEV(B2:B225)

c)

Q1 3.7875 =QUARTILE(B2:B225,1)
Q2 4.765 =QUARTILE(B2:B225,2)
Q3 5.61 =QUARTILE(B2:B225,3)

Q2 (median) > mean
this indicates that data is skewed to the left. for a negatively skewed data, mean < median < mode.

d)

Q1 –1.5*IQR	=3.7875-1.5*(5.61-3.7875)	1.05375
Q3 + 1.5*IQR	=5.61+1.5*(5.61-3.7875)	8.34375

Any point below Q1 –1.5*IQR (1.05375) or above Q3 + 1.5*IQR (8.34375) is an outliers.

there are three outliers in the data: 1, 1, and 1.

data:

Student ID	GPA	sorted data
1	6.75	1
2	3.78	1
3	4.11	1
4	3.64	1.21
5	5.91	1.3
6	5.75	1.35
7	5.35	1.4
8	1.99	1.48
9	4.81	1.59
10	4.09	1.75
11	5.39	1.87
12	5.84	1.94
13	1.59	1.99
14	2.5	2.18
15	4.09	2.31
16	6.52	2.34
17	6.65	2.45
18	7	2.5
19	3.5	2.55
20	5.25	2.66
21	4.06	2.78
22	4.58	2.8
23	5.37	2.9
24	5.18	2.95
25	6.56	2.95
26	5.46	3.13
27	3.93	3.15
28	5.3	3.15
29	1.35	3.16
30	5.6	3.18
31	2.45	3.22
32	4.6	3.23
33	3.36	3.23
34	5.12	3.25
35	6.54	3.29
36	4.95	3.36
37	5.42	3.37
38	4.2	3.37
39	4.88	3.39
40	3.37	3.41
41	3.79	3.41
42	3.13	3.5
43	5.86	3.5
44	6.31	3.5
45	4.81	3.5
46	6.26	3.55
47	4.83	3.57
48	6.42	3.62
49	6.66	3.64
50	5.53	3.65
51	5.53	3.69
52	6.33	3.71
53	3.93	3.71
54	4.46	3.74
55	4.93	3.76
56	5.68	3.78
57	3.71	3.79
58	3.29	3.79
59	4.63	3.83
60	3.22	3.86
61	3.86	3.93
62	5.18	3.93
63	4.23	3.93
64	5.96	3.95
65	5.81	3.95
66	4.74	3.99
67	5.95	3.99
68	4.34	4
69	4.34	4.02
70	1	4.06
71	5.56	4.06
72	5.95	4.09
73	5.61	4.09
74	4.72	4.11
75	5.35	4.14
76	7	4.16
77	6.12	4.18
78	4.91	4.2
79	3.16	4.23
80	6.47	4.25
81	5.04	4.25
82	4.62	4.27
83	5.4	4.27
84	4.93	4.28
85	5.19	4.3
86	4.91	4.34
87	5.81	4.34
88	5.61	4.37
89	6.47	4.37
90	5.35	4.37
91	5.02	4.39
92	3.71	4.39
93	3.95	4.42
94	3.55	4.42
95	4.25	4.46
96	4.37	4.49
97	2.9	4.51
98	5.96	4.51
99	3.41	4.53
100	5.82	4.53
101	2.78	4.56
102	4.3	4.58
103	6.02	4.58
104	2.95	4.6
105	1.3	4.62
106	4.88	4.63
107	1	4.67
108	3.57	4.7
109	3.5	4.72
110	2.34	4.74
111	4.02	4.74
112	5.7	4.76
113	5.49	4.77
114	3.93	4.81
115	1.75	4.81
116	4.86	4.81
117	3.95	4.83
118	3.69	4.83
119	4.95	4.84
120	1	4.86
121	4.37	4.88
122	4.77	4.88
123	4.27	4.9
124	1.94	4.91
125	5.46	4.91
126	3.79	4.93
127	3.5	4.93
128	3.18	4.95
129	5.63	4.95
130	5.39	4.98
131	1.4	5
132	4.51	5
133	3.76	5
134	4.37	5.02
135	3.23	5.02
136	1.87	5.04
137	5.16	5.12
138	6.51	5.12
139	1.21	5.16
140	4.67	5.18
141	4.39	5.18
142	2.55	5.19
143	4.18	5.25
144	5.25	5.25
145	5.86	5.25
146	4.27	5.3
147	5.86	5.35
148	6.65	5.35
149	4.56	5.35
150	4.9	5.35
151	5.74	5.35
152	5.02	5.37
153	5.53	5.37
154	5.37	5.39
155	6.44	5.39
156	5.84	5.4
157	6.05	5.42
158	4.25	5.46
159	4.84	5.46
160	6.4	5.49
161	3.25	5.49
162	3.41	5.53
163	5.35	5.53
164	3.39	5.53
165	5.49	5.56
166	4.98	5.56
167	6.07	5.6
168	5.93	5.61
169	6.82	5.61
170	6.38	5.63
171	6.37	5.65
172	4.83	5.68
173	5	5.7
174	4.39	5.74
175	5	5.75
176	5.84	5.77
177	5.82	5.81
178	6.45	5.81
179	3.15	5.81
180	4.49	5.82
181	3.99	5.82
182	3.5	5.84
183	4.42	5.84
184	2.95	5.84
185	5.35	5.84
186	4.81	5.86
187	4.58	5.86
188	3.74	5.86
189	3.37	5.91
190	5	5.93
191	4.14	5.93
192	2.18	5.95
193	5.56	5.95
194	5.77	5.95
195	4	5.96
196	4.74	5.96
197	4.53	5.96
198	5.93	6.02
199	4.28	6.05
200	4.53	6.07
201	4.51	6.12
202	4.7	6.26
203	4.42	6.31
204	5.25	6.33
205	3.62	6.37
206	3.23	6.38
207	5.84	6.4
208	4.76	6.42
209	7	6.44
210	5.95	6.45
211	5.12	6.47
212	3.83	6.47
213	5.81	6.51
214	5.96	6.52
215	3.15	6.54
216	2.66	6.56
217	4.16	6.65
218	3.65	6.65
219	5.65	6.66
220	2.31	6.75
221	4.06	6.82
222	1.48	7
223	2.8	7
224	3.99	7

orchestra answered 2 years ago

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