1. The ages of a sample of Canadian tourists flying from Toronto to Hong Kong were: 32, 21, 60,
47, 54, 17, 72, 55, 33 and 41. a)Compute the mean. b)Compute the range. c)Compute the
standard deviation. d)Compute the interquartile range. e)Are they any outliers?
Solution
a. The range is simply the largest value minus the smallest value of a
sample. In this case:
Range = 72-17 = 55
b. In order to calculate the mean deviation and the standard
deviation, we must find the mean of this sample. This is:
32+21+60+47+54+17+72+55+33+41
----------------------------- = 43.2
Therefore, using the formula in the link, the mean deviation is:
|32-43.2| + |21-43.2| + |60-43.2| + ... + |41-43.2|
---------------------------------------------------- =
11.2 + 22.2 + 16.8 + ... + 2.2
---------------------------------------------------- = 14.4
So the mean deviation is 14.4
c. Finally, the sample variance is:
(32.2-43.2)^2 + (21-43.2)^2 + ... + (41-43.2)^2
----------------------------------------------- = 310.62
So the sample standard deviation is the square root of this number, that is, 17.62.
d.39.5
e. No outliers