Here are the noon temperatures (in degrees Celsius) in a particular Canadian city on Thanksgiving Day for the 10 years from 2002 through 2011: 0, 3, 6, 8, 2, 9, 7, 6, 4, 5. Describe the typical temperature and the amount of variation to a person who has never had a course in statistics. Give three ways of describing the representative temperature and two ways of describing its variation, explaining the differences and how you figured each. (You will learn more if you try to write your own answer first, before reading our answer at the back of the book.)

a) Three ways of describing the representative or typical temperatures are the mean, median, and mode.

The mean = 5.  This is the average temperature.  It is calculated by adding up the varying temperatures each year and dividing by 10.

Median = 5.5.  This is the middle value in the temperature table.  There are two middle numbers (5 and 6) in the dataset.  They are added and divided by two.

Mode = 6.  This is the value that occurs more than other values in the dataset.  The value 6 occurred twice more than other values.

b) The two ways of describing the variation of temperatures are the variance and the standard deviation.

Variance = 7. This is a measure of how spread out a data set is. It is calculated as the average squared deviation of each number from the mean of a dataset.

Standard Deviation = 2.65.  The standard deviation measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.

Step-by-step explanation:

a) Data and Calculations:

Noon Temperatures (in degrees Celsius) in a particular Canadian City on Thanksgiving Day:

Year    Degree  Difference     Squared

           Celsius                       Difference

2002        0          -5                     25

2003        3          -2                       4

2004        6           1                        1

2005        8           3                       9

2006        2          -3                       9

2007        9           4                      16

2008        7           2                       4

2009        6           1                        1

2010         4          -1                        1

2011          5          0                       0

Sum       50                                  70

Mean =    5 (50/10)

Variance =                                    7 (70/10)

Standard Deviation = 2.65 (Square root of variance)          

Median =  0, 2, 3, 4, 5, 6, 6, 7, 8, 9 (the values are arranged numerically.)

= (5 + 6)/2 = 5.5

Mode = 6 (occurred twice more than other values)

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