Question

3.2.26-т Question Help Use the magnitudes (Richter scalo) of the 120 earthquakes listed in the accompanying data table. Use technology to find the range, variance, and standard deviation.If another value, 7.00, is added to those listed in the data set, do the measures of variation change much? Magnitudes 3.32 2.77 2.78 1.95 1.67 2.54 2.42 3.42 3.94 1.58 290 1.63 2.56 3.97 2.53 245 1.85 2.18 2.42 2.98 2.94 2.36 198 3.05 2.39 3.43 3.45 1.55 2.53 1.50 2.19 3.06 2.30 3.26 1.96 1.92 2.38 2.95 2.56 1.49 2.16 2.33 .92 2.70 2.92 1.83 3.64 2.67 1.45 3.58 3.17 2.59 1.54 1.43 2.86 2.88 2.19 1.67 3.17 1.38 1.71 2.35 1.14 2.36 2.49 1.78 .97 3.00 1.95 2.44 1.86 2.26 2.32 322 4.03 2.08 1.50 2.29 2.34 2.58 2.56 2.19 2.75 2.46 2.68 365 2.83 2.77 3.29 1.76 4.67 321 2.38 2.01 3.88 2:38 2.86 267 2.30 2.81 2.75 2.42 3.39 2.34 1.50 2.40 2.42 2.46 2.69 244 2.81 2.64 2.70 2.43 Print Done Check Answer

Answer 1

I am going to be using excel to answer this question:

(I had to type in a lot of numbers, I have cross verified them too but in case I made a mistake let me know in comments). Also calculating the sample variance and standard deviation.

Count	120
Mean	2.5225
Maximum	4.67
Minimum	1.14
Range	3.53
Variance	0.425305
Standard Deviation	0.652154

For the data:

Data
3.32
2.77
2.78
1.95
1.87
2.54
2.42
3.42
3.94
1.58
2.9
1.63
2.56
3.97
2.53
2.45
1.85
2.18
2.42
2.98
2.94
2.36
1.98
3.05
2.8
3.89
2.98
2.1
1.84
2.33
2.39
3.43
3.45
1.55
2.53
1.5
2.19
3.06
2.3
3.26
1.96
1.92
2.38
2.95
2.56
1.49
2.16
2.33
1.92
2.7
2.92
1.83
3.64
2.67
1.45
3.58
3.17
2.59
1.54
1.43
2.86
2.88
2.19
1.67
3.17
1.38
1.71
2.35
1.14
2.36
2.49
1.78
1.97
3
1.95
2.44
1.86
2.26
2.32
3.22
4.03
2.08
1.5
2.29
2.34
2.58
2.56
2.19
2.75
2.46
2.68
3.65
2.83
2.77
3.29
1.76
4.67
3.21
2.38
2.01
3.88
2.38
2.86
2.67
2.3
2.81
2.75
2.42
3.39
2.34
1.5
2.4
2.42
2.46
2.89
2.44
2.81
2.64
2.7
2.43

Adding 7 leads to the following results:

Count	121
Mean	2.559504
Maximum	7
Minimum	1.14
Range	5.86
Variance	0.587446
Standard Deviation	0.766451

So yes the measures of variance do change by a considerable amount due to these outliers.

Let me know in comments if anything is unclear. Will reply ASAP. Please upvote!