Question

Science MajorsA bank has collected data on the opening balances of new home loans issued in the final quarter of 2018. The dataset of 200 observations is contained in the file: Home Loans (THA 1).xlsx. Based on the data, answer the following questions.

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

Obs	Home Loan, Open. Bal.
1	544,723
2	686,461
3	422,582
4	373,228
5	369,600
6	353,011
7	259,339
8	236,532
9	496,713
10	1,052,824
11	454,077
12	806,701
13	482,691
14	920,000
15	444,720
16	780,000
17	377,858
18	366,611
19	283,918
20	216,536
21	291,182
22	776,145
23	375,723
24	403,552
25	342,989
26	191,632
27	800,350
28	268,200
29	519,466
30	293,192
31	414,739
32	352,222
33	258,587
34	228,633
35	329,476
36	324,013
37	239,375
38	489,659
39	279,174
40	457,456
41	409,731
42	1,332,051
43	367,738
44	331,450
45	364,676
46	472,790
47	332,199
48	525,831
49	393,803
50	291,081
51	469,585
52	363,128
53	360,221
54	290,435
55	452,734
56	493,088
57	362,044
58	232,913
59	367,991
60	451,662
61	495,394
62	473,753
63	245,583
64	212,484
65	495,633
66	348,539
67	380,756
68	395,000
69	554,626
70	346,094
71	482,000
72	279,040
73	431,405
74	712,740
75	479,868
76	632,612
77	334,365
78	290,458
79	583,572
80	311,145
81	406,683
82	234,646
83	236,695
84	239,475
85	877,764
86	559,089
87	278,475
88	1,005,103
89	341,572
90	235,907
91	347,033
92	452,277
93	542,540
94	859,707
95	426,113
96	451,640
97	275,643
98	461,818
99	273,911
100	332,744
101	625,000
102	313,953
103	246,979
104	556,798
105	223,566
106	434,694
107	330,051
108	528,349
109	296,459
110	673,742
111	255,977
112	497,893
113	173,452
114	364,564
115	423,801
116	412,745
117	344,350
118	375,594
119	576,789
120	384,224
121	454,949
122	429,826
123	372,453
124	375,593
125	502,794
126	426,347
127	448,161
128	223,132
129	459,372
130	522,012
131	297,186
132	343,947
133	648,363
134	121,147
135	288,658
136	269,492
137	1,310,311
138	167,636
139	377,545
140	564,538
141	1,113,770
142	442,390
143	258,433
144	433,609
145	256,726
146	249,058
147	258,709
148	244,828
149	581,815
150	344,052
151	331,641
152	303,224
153	328,384
154	187,425
155	312,951
156	476,582
157	951,336
158	284,487
159	400,050
160	536,902
161	439,255
162	266,541
163	263,611
164	442,662
165	557,690
166	375,426
167	337,402
168	240,806
169	367,070
170	621,110
171	317,486
172	266,651
173	466,251
174	304,040
175	297,971
176	199,448
177	340,568
178	236,054
179	500,615
180	187,737
181	330,010
182	1,340,394
183	365,058
184	396,187
185	375,523
186	435,712
187	426,242
188	407,575
189	301,040
190	380,631
191	280,846
192	393,315
193	217,536
194	457,019
195	180,584
196	636,068
197	247,106
198	1,458,183
199	434,295
200	462,356

Answer 1

Obs	sorted data
1	121,147
2	167,636
3	173,452
4	180,584
5	187,425
6	187,737
7	191,632
8	199,448
9	212,484
10	216,536
11	217,536
12	223,132
13	223,566
14	228,633
15	232,913
16	234,646
17	235,907
18	236,054
19	236,532
20	236,695
21	239,375
22	239,475
23	240,806
24	244,828
25	245,583
26	246,979
27	247,106
28	249,058
29	255,977
30	256,726
31	258,433
32	258,587
33	258,709
34	259,339
35	263,611
36	266,541
37	266,651
38	268,200
39	269,492
40	273,911
41	275,643
42	278,475
43	279,040
44	279,174
45	280,846
46	283,918
47	284,487
48	288,658
49	290,435
50	290,458
51	291,081
52	291,182
53	293,192
54	296,459
55	297,186
56	297,971
57	301,040
58	303,224
59	304,040
60	311,145
61	312,951
62	313,953
63	317,486
64	324,013
65	328,384
66	329,476
67	330,010
68	330,051
69	331,450
70	331,641
71	332,199
72	332,744
73	334,365
74	337,402
75	340,568
76	341,572
77	342,989
78	343,947
79	344,052
80	344,350
81	346,094
82	347,033
83	348,539
84	352,222
85	353,011
86	360,221
87	362,044
88	363,128
89	364,564
90	364,676
91	365,058
92	366,611
93	367,070
94	367,738
95	367,991
96	369,600
97	372,453
98	373,228
99	375,426
100	375,523
101	375,593
102	375,594
103	375,723
104	377,545
105	377,858
106	380,631
107	380,756
108	384,224
109	393,315
110	393,803
111	395,000
112	396,187
113	400,050
114	403,552
115	406,683
116	407,575
117	409,731
118	412,745
119	414,739
120	422,582
121	423,801
122	426,113
123	426,242
124	426,347
125	429,826
126	431,405
127	433,609
128	434,295
129	434,694
130	435,712
131	439,255
132	442,390
133	442,662
134	444,720
135	448,161
136	451,640
137	451,662
138	452,277
139	452,734
140	454,077
141	454,949
142	457,019
143	457,456
144	459,372
145	461,818
146	462,356
147	466,251
148	469,585
149	472,790
150	473,753
151	476,582
152	479,868
153	482,000
154	482,691
155	489,659
156	493,088
157	495,394
158	495,633
159	496,713
160	497,893
161	500,615
162	502,794
163	519,466
164	522,012
165	525,831
166	528,349
167	536,902
168	542,540
169	544,723
170	554,626
171	556,798
172	557,690
173	559,089
174	564,538
175	576,789
176	581,815
177	583,572
178	621,110
179	625,000
180	632,612
181	636,068
182	648,363
183	673,742
184	686,461
185	712,740
186	776,145
187	780,000
188	800,350
189	806,701
190	859,707
191	877,764
192	920,000
193	951,336
194	1,005,103
195	1,052,824
196	1,113,770
197	1,310,311
198	1,332,051
199	1,340,394
200	1,458,183

total sum =ΣX=   85045831   ,   n=   200
mean =    ΣX/n =    425229.155  

Q2 , Median=0.5(n+1)th value =    0.5*201 = 100.5 value of sorted data = 0.5*(100th +101th value ) =   375558      
   

-----------------------

mean>median , data is right skewed

mean <median ,data is left skewed

mean=median , data is symmetric

as we can that mean is greater than median , it means, data is not symmetric

It is skewed to right.