Question

1. The law requires coal mine operators to test the amount of dust in the atmosphere of the mine. A laboratory carries out the test by weighing filters that have been exposed to the air in the mine. The data in the table shows the repeated weighings of the same filter. 1.09 1.92 2.31 1.79 2.28 1.74 1.47 1.97 0.85 1.24 1.58 2.03 1.7 2.17 2.55 2.11 1.86 1.9 1.68 1.51 1.64 0.72 1.69 1.85 1.82 1.79 2.46 1.88 2.08 1.67 1.37 1.93 1.4 1.64 2.09 1.75 1.63 2.37 1.75 1.69 a) Calculate the sample mean, sample variance, and standard deviation. (15 pts) b) Construct a box plot of the data set and comment on the possible presence of outliers

Answer 1

a)

	X	X2
	1.09	1.188
	1.92	3.686
	2.31	5.336
	1.79	3.204
	2.28	5.198
	1.74	3.028
	1.47	2.161
	1.97	3.881
	0.85	0.723
	1.24	1.538
	1.58	2.496
	2.03	4.121
	1.7	2.890
	2.17	4.709
	2.55	6.503
	2.11	4.452
	1.86	3.460
	1.9	3.610
	1.68	2.822
	1.51	2.280
	1.64	2.690
	0.72	0.518
	1.69	2.856
	1.85	3.423
	1.82	3.312
	1.79	3.204
	2.46	6.052
	1.88	3.534
	2.08	4.326
	1.67	2.789
	1.37	1.877
	1.93	3.725
	1.4	1.960
	1.64	2.690
	2.09	4.368
	1.75	3.063
	1.63	2.657
	2.37	5.617
	1.75	3.063
	1.69	2.856
Total	70.97	131.864

Sample mean is calculated as :

Sample variance is calculated as :

Sample standard deviation is :

b)

There are in total 2 outliers present in the data : 0.72 and 0.85

These are extreme values of weighings of the same filter which are not usual.