Question

Use the magnitudes​ (Richter scale) of the earthquakes listed in the data set below. Find the mean and median of this data set. Is the magnitude of an earthquake measuring 7.0 on the Richter scale an outlier​ (data value that is very far away from the​ others) when considered in the context of the sample data given in this data​ set? Explain. Find the mean and median of the data set using a calculator or similar data analysis technology.

2.83 0.48 1.95 0.59 2.78 1.34 0.04 0.83 0.96 0.36

1.36 1.81 2.67 1.53 2.66 1.39 0.99 0.38 2.44 0.33

2.93 1.07 2.61 0.01 1.18 2.35 1.06 2.78 2.47 0.54

2.18 2.94 0.37 1.95 2.79 1.57 2.82 0.76 2.96 2.98

2.13 1.04 0.17 1.78 0.98 2.72 1.99 1.35 1.73 0.03

Is the magnitude of an earthquake measuring 7.0 on the Richter scale an outlier when considered in the context of the sample data​ given?

Answer 1

putting above data in ascending order:

s. no	x
1	0.01
2	0.03
3	0.04
4	0.17
5	0.33
6	0.36
7	0.37
8	0.38
9	0.48
10	0.54
11	0.59
12	0.76
13	0.83
14	0.96
15	0.98
16	0.99
17	1.04
18	1.06
19	1.07
20	1.18
21	1.34
22	1.35
23	1.36
24	1.39
25	1.53
26	1.57
27	1.73
28	1.78
29	1.81
30	1.95
31	1.95
32	1.99
33	2.13
34	2.18
35	2.35
36	2.44
37	2.47
38	2.61
39	2.66
40	2.67
41	2.72
42	2.78
43	2.78
44	2.79
45	2.82
46	2.83
47	2.93
48	2.94
49	2.96
50	2.98
total	79.96
average	1.5992

mean =1.5992

median =middle value =(n+1)/2 th value =(1.53+1.57)/2 =1.55

Q1 =(n+1)/4 th value =(50+1)/4 th vale =0.8125

Q3 =(n+1)*3/4 th value =(50+1)*3/4 th vale =2.6225

hence outer fence =Q3+1.5*(Q3-Q1)=5.3375

as earthquake measuring 7.0 falls outside outer fence ; therefore it is an outlier.