Answer:
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)
