Question

The percentage of cotton in material used to manufacture men's shirts follows. Construct a stem-and-leaf display for the data. Calculate the median and quartiles of these data. Choose the correct answer.

33.6 37.0 34.0 32.1 33.5 35.6 34.9 35.4 32.2 36.1 34.7 32.4 33.9 36.8 32.3 33.7 34.8 36.9 34.4 33.5 33.5 37.5 32.6 34.9 35.8 32.9 35.0 37.2 35.3 35.2 32.7 33.2 36.9 34.7 36.9 33.9 34.7 36.0 34.0 35.1 34.0 36.5 36.8 32.1 35.9 32.6 36.0 36.7 34.1 34.2 35.9 32.9 34.8 32.3 36.8 35.0 32.0 36.0 33.4 33.8 34.6 34.7 36.2 34.1

Answer 1

putting above data in ascending order:

s. no	x
1	32
2	32.1
3	32.1
4	32.2
5	32.3
6	32.3
7	32.4
8	32.6
9	32.6
10	32.7
11	32.9
12	32.9
13	33.2
14	33.4
15	33.5
16	33.5
17	33.5
18	33.6
19	33.7
20	33.8
21	33.9
22	33.9
23	34
24	34
25	34
26	34.1
27	34.1
28	34.2
29	34.4
30	34.6
31	34.7
32	34.7
33	34.7
34	34.7
35	34.8
36	34.8
37	34.9
38	34.9
39	35
40	35
41	35.1
42	35.2
43	35.3
44	35.4
45	35.6
46	35.8
47	35.9
48	35.9
49	36
50	36
51	36
52	36.1
53	36.2
54	36.5
55	36.7
56	36.8
57	36.8
58	36.8
59	36.9
60	36.9
61	36.9
62	37
63	37.2
64	37.5

below is stem leaf graph:

stem		Leaves
32		0 1 1 2 3 3 4 6 6 7 9 9
33		2 4 5 5 5 6 7 8 9 9
34		0 0 0 1 1 2 4 6 7 7 7 7 8 8 9 9
35		0 0 1 2 3 4 6 8 9 9
36		0 0 0 1 2 5 7 8 8 8 9 9 9
37		0 2 5

median =middle value =(64+1)/2 th value =32.5 th value=34.7

Quartile 1 =npth value =64*0.25 th value =16 th value =(33.5+33.5)/2 =33.5

Quartile 3 =npth value =64*0.75 th value =48 th value =(35.9+36)/2 =35.95