Download Statistics 5 - Comparing Normal Distributions

Math 20-2
Statistics: Lesson #5
Comparing Normally Distributed Data
Objective: By the end of the lesson, you should be able to:
- Compare the properties of two or more normally distributed data sets.
Key Point: The height, width, and position on the horizontal axis of a normal curve changes
depending on the mean and standard deviation.
e.g. 1) A men’s and women’s baseball team flew to the North American Indigenous Games.
The members of each team had carry-on luggage for their sports equipment. The masses
of the carry-on luggage were normally distributed with the characteristics shown in the
table below:
Team
 (kg)
 (kg)
Men
6.5
1.0
Women
6.5
0.5
a) Sketch a normal curve to show the distribution of the masses of the carry-on luggage
for each team. Draw both curves on the same grid.
Remember: The area
under each curve has
to be the same: 100%
of the data.
b) The women’s team won the championship. Each member received a medal and a
souvenir baseball, with a combined mass of 1.0 kg, which they packed in their carryon luggage. Sketch a graph to show how the distribution of the masses of the
women’s carry-on luggage changed for their flight home.
Math 20-2
Statistics: Lesson #5
Summary: How does a change in mean and standard deviation affect a normal curve?

Change in mean (  ) –

Change in standard deviation (  ) –
e.g. 2) Consider the following four graphs of normal distributions, drawn using the same scale.
Rank them in order of increasing standard deviation.
Assignment:
p. 279-282 #1, 6-7, 9-11, 14, 16