Statistics problem

Question

Refer to the data set of times, in minutes, required for an airplane to taxi out for takeoff, listed below.

 

47, 50, 46, 28, 48, 34, 46, 45, 17, 45, 16, 16
14, 23, 27, 50, 46, 12, 27, 22, 13, 48, 24, 23
29, 17, 47, 17, 22, 27, 25, 48, 46, 50, 27, 11
18, 39, 18, 39, 49, 4928, 20, 24, 27, 35, 44

 

Find the mean and

median.

How is it helpful to find the mean?

Answer 1

Recall the mean is x_bar = (∑ x_i) / n

 

For a dataset of this size, it is best to put it into a calculator in statistics mode or use statistics software.

 

There mean is

 

(47 + 50 + ... + 35 + 44) / 47 = 6374 / 47 ≈ 135.617

 

For the median, you need to sort the numbers first to get

 

11, 12, 13, 14, 16, 16, 17, 17, 17, 18, 18, 20,
22, 22, 23, 23, 24, 24, 25, 27, 27, 27, 27, 27,
28, 29, 34, 35, 39, 39, 44, 45, 45, 46, 46, 46,
46, 47, 47, 48, 48, 48, 49, 50, 50, 50, 4928

 

The middle number in the sorted list is the median, which is 27.

 

In this case, knowing the mean is helpful because it is so much bigger than the median. The difference this big is usually due to an outlier.

 

In this case, the outlier is clearly 4928.

 

From the data, it is most likely that a comma was forgotten and the 4928 really was meant to be two numbers, 49 and 28.

 

This would have made there be 48 pieces of data.

 

Then, recalculating gives a mean of 1523 / 48 ≈ 31.729 and median (27+28) / 2 = 27.5

 

Now the mean and median are close together, with only a slight right-skewness.