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MDM4U Chapter 3 Review
Normal Distribution
Mr. Lieff
3.1 Graphical Displays
 name and be able to interpret the various
types of distributions

ex: when would we use a histogram vs. a bar
graph?




Histogram necessary for continuous data
Bar graph for qualitative data
Discrete data  depends on the spread
ex: how do you calculate bin width?

(range) ÷ (# of bars)
3.2 Central Tendency
 Be able to calculate mean, median, mode
and weighted mean

ex: determine which measure is appropriate
 Be aware of the effect of outliers

Affect the mean more than the median
 Recognize the location of the measures with
respect to skewed distributions


if mode < median < mean…right skew
If mean < median < mode…left skew
3.3 Measures of Spread
 Be able to calculate and interpret range, IQR
and (population) standard deviation





Up to 6 data points for std.dev.
A larger value for any measure of spread
(range, IQR, std.dev.) means the data has
more spread
range gives the size of the interval containing
all of the data
IQR gives the size of the interval containing
the middle 50% of the data
Std dev measures the variation from the mean
3.3 Measures of Spread cont’d
 How to calculate IQR
Order the data!!!
 Find the median, Q2
 Find the 1st half median, Q1
 Find the 2nd half median, Q3
 IQR = Q3 – Q1
 How to calculate Std.dev.
 Find the mean
 Find the deviations (data – mean)
 Square the deviations
 Average the deviations  variance σ2
 Take square root  std. dev. σ

3.4 Normal Distribution
 Be familiar with the characteristics of a
Normal Distribution (68–95–99.7% rule)
 Calculate the ranges of expected data based
on 1, 2 or 3 std.dev. above and/or below the
mean
 Ex: If a set of data has mean 10 and standard
deviation 2, what percent of the data lie
between 6 and 14?
 ans: 6 is 2 std dev below the mean and 14 is
2 std dev above. So 95% of the data falls in
the range (see diagram)
Normal Distribution
99.7%
95%
68%
X ~ N ( x, 2 )
34%
34%
0.15%
13.5%
13.5%
2.35%
2.35%
x - 3σ
x - 2σ
0.15%
x - 1σ
x
x + 1σ
x + 2σ
x + 3σ
Normal Distribution
 Ex: If a set of data has mean 10 and standard
deviation 2, what percent of the data lie
between 8 and 14?
 Ans: 34% + 34% + 13.5% = 81.5%
3.5 Z-Scores
 Standard normal distribution X ~ N (0,12 )
 mean 0, std dev 1
x
 1) Be able to calculate a z-score
z
x

 2) Be able to calculate the % of data below / above a
value (z-table)
 3) Given the standard deviation and the mean, be
able to calculate the percentile for a piece of data
(round z-table pct to whole number)
 4) Be able to calculate the percent of data between 2
population values
3.5 Z-Scores
 Ex: Given that X~N(10,22), what percent of
the population is between 7 and 11?
 Ans: calculate z-scores for the two data
values, look up their respective percents in
the z-table and subtract
 for 7: z = (7 – 10)/2 = -1.5 => 6.68%
 for 11: z = (11-10)/2 = 0.5 => 69.15%
 69.15 – 6.68 = 62.47
 so 62.47% of the data lies between these two
values
3.6 Mathematical Indices
 These are arbitrary numbers that provide a
measure of something
 e.g. BMI, Slugging Percentage, Moving
Average
 You should be able to work with a given
formula and interpret the meaning of
calculated results
Review
 p. 199 #1a, 3a, 4-6
 20 Marks MC
 30 marks Short Answer / Problem
 You will be provided with:


Formulas in Back Of Book
z-score table on p. 398
 Tomorrow: bring an object of chance (coin,
cards, dice, spinner, etc.)