Statistical Reasoning
Statistical reasoning is the way people reason with statistical ideas and make sense of statistical information.
Exploring Data
When you want to represent a set of data by using only one number, you use a measure of central tendency. The 3 most common measures of central tendency are:
1.
___________ - The mean is the “_______________” of a set of data. You can calculate the mean by dividing the sum of the values divided by the total number of values in the data set. So…
2.
____________ - The median is the ________________ number in the data set. Note: if your data is not in order from smallest to largest, you must rearrange it!
**Note: What happens if there are 2 middle numbers? When would this occur?
3.
____________ - the value that occurs frequently. A data set can have 0 modes, 1 mode, or more than 1 mode. To determine the mode, simply just find the number that the most often.

We can also look at the dispersion of the data – how spread out the data is. A common dispersion that we will look at is the . This is the difference between the and the
numbers in the data set.
Examples:
1.
What measure of central tendency would an advertiser have used if the following claims were made? a.
Pepsi, the people’s choice. b.
The average age of those participating in the marathon was 27.6 years. c.
Most accidents in the city occur between 4:30 pm and 5:30 pm. d.
Half the class scored higher than 61%.

2.
Given below are two charts that show the average daily temperatures for 2 Canadian cities –
Langley, BC and Windsor, ON.
Average Daily Temperatures in Langley, BC
Month Jan. Feb. Mar. Apr. May Jun. Jul. Aug Sep. Oct. Nov. Dec.
2.2 4.4 6.3 8.6 11.8 14.2 16.7 17.0 14.2 9.8 5.1 2.7 Average
Daily
Tempera- ture (ᵒC)
Average Daily Temperatures in Windsor, ON
Month Jan. Feb. Mar. Apr. May Jun. Jul. Aug Sep. Oct. Nov. Dec.
-4.5 -3.2 2.0 8.2 14.9 20.1 22.7 21.6 17.4 11.0 4.6 -1.5 Average
Daily
Tempera- ture (ᵒC) a.
Construct a graph to illustrate the average daily temperatures in Langley and Windsor.

b.
Determine the range, mean, median, and mode for the average daily temperatures in the 2 cities. c.
Compare your graph and the results from part “b” to compare the temperatures in the two cities. d.
Why might you want to compare the two sets of data?