Question

3.273.27	2.822.82	2.832.83	1.941.94	1.671.67	2.502.50
2.432.43	3.413.41	3.933.93	1.601.60	2.882.88	1.601.60
2.562.56	3.943.94	2.532.53	2.452.45	1.841.84	2.192.19
2.432.43	3.003.00	2.902.90	2.372.37	1.991.99	3.043.04
2.812.81	3.843.84	2.962.96	2.072.07	1.851.85	2.362.36
2.402.40	3.453.45	3.423.42	1.541.54	2.562.56	1.491.49
2.222.22	3.063.06	2.282.28	3.233.23	1.961.96	1.921.92
2.402.40	2.962.96	2.562.56	1.491.49	2.152.15	2.332.33
1.921.92	2.722.72	2.882.88	1.821.82	3.683.68	2.692.69
1.431.43	3.643.64	3.123.12	2.552.55	1.531.53	1.421.42
2.852.85	2.842.84	2.192.19	1.671.67	3.173.17	1.381.38
1.741.74	2.372.37	1.131.13	2.342.34	2.492.49	1.791.79
2.002.00	3.013.01	1.931.93	2.412.41	1.881.88	2.232.23
2.362.36	3.193.19	4.004.00	2.092.09	1.501.50	2.302.30
2.312.31	2.612.61	2.562.56	2.222.22	2.752.75	2.462.46
2.692.69	3.593.59	2.802.80	2.742.74	3.283.28	1.731.73

Use the magnitudes​ (Richter scale) of the

120120

earthquakes listed in the accompanying data table. Use technology to find the​ range, variance, and standard deviation. If another​ value,

7.507.50​,

is added to those listed in the data​ set, do the measures of variation change​ much?

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Without the extra data​ value, the range is

Answer 1

Note: There are 96 values and not 120

1.) For Range

Minimum value: min( < data_range >) = 1.13

Maximum value: max( < data_range >) = 4

Range = max - min = 2.87

2.) For variance of sample

Assuming the data is from sample

Formula: var.s( < data_range >) = 0.426

3.) For Standard deviation:

Assuming the data is from sample

Formula: stdev.s( < data_range >) = 0.653

Lets add the value 7.50 to the data:

1.) For Range

Minimum value: = 1.13

Maximum value: = 7.5

Range = max - min = 6.37

2.) For variance of sample

Assuming the data is from sample

Variance = 0.683

3.) For Standard deviation:

Assuming the data is from sample

SD = 0.826

Yes the measures of variation change a lot after adding the extra value. This value is an outlier compared to the data present in the table and hence its affects the measures of variation.