Question

Calculate the variance and the standard deviation.

The Department of Transportation (DOT) fields thousands of complaints about airlines each year. The DOT categorizes and tallies complaints, and then periodically publishes rankings of airline performance. The following table presents the 2006 results for the 10 largest U.S. airlines.

a. Which airline fielded the least amount of complaints? Which airline fielded the most? Calculate the range.

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b. Calculate the mean and the median number of complaints for this sample.

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c. Calculate the variance and the standard deviation.

Answer 1

The data is related to the department of Transportation fields thousands of complaints about airlines each year.

The following table presents the 2006 results for the 10 largest U.S airlines.

a)

Southwest Airlines fielded has less number of complaints which is 1.82. United Airlines has maximum number of complaints which is 13.60.

Calculate the range.

b)

Calculate mean number of complaints for the given sample.

The mean is,

The mean number of complaints fielded by the sample is 8.336.

Calculate median number of complaints for the given sample.

Median is central value. Since the observations are even number of observations (10).

So the median is the average of and observation of order set.

First, arrange the data in ascending order.

Therefore, the median is,

Calculate Sample variance.

The formula of Sample variance is,

The following table shows the computation of Sample variance.

1.82	-6.54	42.7716
3.98	-4.38	19.1844
5.24	-3.12	9.7344
6.24	-2.12	4.4944
8.83	0.47	0.2209
8.84	0.48	0.2304
10.35	1.99	3.9601
10.87	2.51	6.3001
13.59	5.23	27.3529
13.6	5.24	27.4576

Therefore, the sample variance is,

Calculate the standard deviation.

Therefore, the variance and standard deviation are