Chapter 3 Review
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Transcript Chapter 3 Review
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.)