1. Summary of Distributions of Data Investigation
MAP4C – Statistics
Summary of Distributions
of Data Investigation

2. Data Set A The data in set A approximates a normal distribution.
What is a normal distribution?
This distribution is often referred to as a “bell curve” because of its shape.

3. Data Set A
The mean, median and the mode are all equal in a normal distribution and are located at the center of the distribution.
The normal distribution is symmetrical around the mean.

4. Data Set B
The data in set B follows a bimodal distribution. This distribution has two high peaks and, if the peaks are of equal height, they represent the two modes.

5. Data Set B
The mean and median are not necessarily equal and are located between the two peaks.
A bimodal distribution often indicates there are two subgroups in the data, which should be examined independently.
In our investigation, the data on masses of adult men should be considered separately from the data of adult women.

6. Data Set C & D The distributions of data sets C and D are both skewed.
A skewed distribution is not symmetrical. The data tends to be clustered at one end.

7. Data Set C
The distribution of the data in set C is an example of a distribution that is skewed left also referred to as a negative skew.
Although the peak of the distribution is on the right hand side of the data, it is skewed left because there is a long tail to the left.
In a distribution that is skewed left, the mode is located at the peak, the median is less than the mode, and the mean is less than the median.
The mean is affected by the extreme values in the tail. (ie: possible outliers)

8. Data Set D
The distribution of the data in set D is an example of a distribution that is skewed right also referred to as a positvie skew.
Although the peak of the distribution is on the left hand side of the data, it is skewed right because there is a long tail to the right.
In a distribution that is skewed right, the mode is located at the peak, the median is greater than the mode, and the mean is greater than the median.
The mean is affected by the extreme values in the tail. (ie: possible outliers)

9. Example
A grade 12 student in MAP4C plans to collect data on the heights (in cm) of all the people in each of these groups at their school. Predict the type of distribution that would be seen?
the members of the senior girls basketball team.
The male students in grade 11.
All the students in the entire school.

10. Trumping the Teachers
Some teachers took a plane trip to a national convention. While on the plane they were discussing their salaries and noted that most of them made similar salaries.
Ten made $ and ten made $
This made the average salary $

11. Continued…
A passenger joined the flight because his private jet had engine trouble. Word soon spread throughout the plane that this passenger was Donald Trump.
One bold teacher asked “The Donald” to compare his annual salary to theirs.
Mr. Trump replied that his estimated yearly income was about $

12. Do the Math?
What happened to the average of the salaries now that Trump joined the group?

13. Continued… Do you see how much difference one score can make?
Neither the teachers salaries nor Trump’s salary was anywhere near the average.
Compare this to when a students earns a bad test score.
We call this result an outlier and it skews the data.