Question

The table represents the answers of 80 respondents to the survey “How much sports
trainings do you have every year?” carried out among college students. Construct a stem-and-leaf
diagram for the data. Calculate the median and quartiles of these data.

129 157 154 191 192 142 188 126 128 180
190 166 157 147 155 154 200 128 167 143
131 156 153 168 149 144 155 188 149 142
160 149 184 187 169 161 157 134 122 173
188 183 178 148 135 188 187 166 121 177
169 182 158 169 146 173 133 189 183 143
148 121 181 145 189 120 122 189 146 190
128 142 189 131 199 182 197 148 157 140

Answer 1

Here to construct stem and leaf diagram , we have considered , stem unit =   10 and leaf unit =   1.

Stem	Leaf
12	0 1 1 2 2 6 8 8 8 9
13	1 1 3 4 5
14	0 2 2 2 3 3 4 5 6 6 7 8 8 8 9 9 9
15	3 4 4 5 5 6 7 7 7 7 8
16	0 1 6 6 7 8 9 9 9
17	3 3 7 8
18	0 1 2 2 3 3 4 7 7 8 8 8 8 9 9 9 9
19	0 0 1 2 7 9
20	0

Here is list of sorted data set values in ascending order, and their five number summary.

Location	Training	Five Number Summary
1	120	<-- Minimum = 120
2	121
3	121
4	122
5	122
6	126
7	128
8	128
9	128
10	129
11	131
12	131
13	133
14	134
15	135
16	140
17	142
18	142
19	142
20	143	First Quartile = mid value of first half of ordered data set = 20th + 21st location value / 2 = (143+143)/2= 143
21	143
22	144
23	145
24	146
25	146
26	147
27	148
28	148
29	148
30	149
31	149
32	149
33	153
34	154
35	154
36	155
37	155
38	156
39	157
40	157	Median = Values at mid location for sorted data value i.e. At 40th and 41st location = (157 + 157 ) / 2 = 157
41	157
42	157
43	158
44	160
45	161
46	166
47	166
48	167
49	168
50	169
51	169
52	169
53	173
54	173
55	177
56	178
57	180
58	181
59	182
60	182	Third Quartile = mid value of second half of ordered data set = 60th + 61st location value / 2 = (182+183)/2= 182.5
61	183
62	183
63	184
64	187
65	187
66	188
67	188
68	188
69	188
70	189
71	189
72	189
73	189
74	190
75	190
76	191
77	192
78	197
79	199
80	200	<-- Maximum = 200

Here is summary of median and quartiles.

Median = average values of mid location for sorted data value i.e. At 40th and 41st location = (157 + 157 ) / 2 = 157

First Quartile = mid value of first half of ordered data set = 20th + 21st location value / 2 = (143+143)/2= 143

Third Quartile = mid value of second half of ordered data set = 60th + 61st location value / 2 = (182+183)/2= 182.5

Interquartile range = Third quartile value - First Quartile Value .

Interquartile range = 182.5 - 143= 39.5