The sample of eight companies in the aerospace industry was surveyed as to their

Question

The sample of eight companies in the aerospace industry was surveyed as to their return on investment last year. The results are: 10.6, 12.6, 14.8, 18.2, 12.0, 14.8, 12.2, and 15.6. 1. Compute the variance using the deviation formula. 2. Compute the variance using the direct formula. 3. Determine the sample standard deviation. The sample of eight companies in the aerospace industry was surveyed as to their return on investment last year. The results are: 10.6, 12.6, 14.8, 18.2, 12.0, 14.8, 12.2, and 15.6. 1. Compute the variance using the deviation formula. 2. Compute the variance using the direct formula. 3. Determine the sample standard deviation.

Explanation / Answer

1) Mean = (10.6 + 12.6 + 14.8 + 18.2 + 12 + 14.8 + 12.2 + 15.6) / 8 = 13.85

Population variance = [(10.6 - 13.85)2 + (12.6 - 13.85)2 + (14.8 - 13.85)2 + (18.2 - 13.85)2 + (12 - 13.85)2 + (14.8 - 13.85)2 + (12.2 - 13.85)2 + (15.6 - 13.85)2 ] / 8 = 5.2575

2) variance = (range / 4)2 = ((18.2 - 10.6) / 4)2 = 3.61

3) Sample variance = [(10.6 - 13.85)2 + (12.6 - 13.85)2 + (14.8 - 13.85)2 + (18.2 - 13.85)2 + (12 - 13.85)2 + (14.8 - 13.85)2 + (12.2 - 13.85)2 + (15.6 - 13.85)2 ] / 7 = 6.0086

Sample standard deviation = sqrt(6.0086) = 2.45

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