The ages of a sample of Canadian tourists flying from Toronto to Hong Kong were: 31, 23, 57, 41, 52, 14, 77, 51, 34, 40 (Round range to nearest whole number and standard deviation to 2 decimal places.)
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a. | Compute the range. |
Range |
b. | Compute the standard deviation. |
Standard deviation |
Explanation:
a.
b.
The range is the difference between the largest and smallest value or 63, found by 77 – 14.
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b.
The sample mean is 13.80, found by 138/10 where = 42.00
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The
differences between each value and the mean are: -11.0, -19.0, 15.0,
-1.0, 10.0, -28.0, 35.0, 9.0, -8.0 and -2.0, respectively. Their squares
are 121.00, 361.00, 225.00, 1.00, 100.00, 784.00, 1,225.00, 81.00,
64.00, and 4.00. The sum of the squares is 2,966.0. So the sample
variance is 329.556, found by 2,966.0/9 and the sample standard
deviation is the square root of that number or 18.1537.
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