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```MBF3C 3.6 Common Distributions
Standard deviation should be looked at with respect to the
mean.
Let’s say the standard deviation for the prices of telescopes
is \$50.
If the mean price is \$200, then the standard deviation
indicates a wide spread in the selling price.
If the mean price was \$1200, then the standard deviation
indicates little variance in the selling price.
One way to analyze data is to look at frequency, or the
number of times, each value occurs.
Ex: A driving test for a class of students had the following
results out of 100, and whole marks were awarded.
Mark
30-40 40-50 50-60 60-70 70-80 80-90 90-100
# of students
1
6
19
32
21
16
5
A bar graph showing the frequency of the marks:
Driving Test Marks
35
30
25
20
15
10
5
0
30-40
40-50
50-60
60-70
70-80
80-90
90-100
We begin to see a distribution of data as a mountain peak
arrangement. (approximated on graph through mid-points of
each bar)
If we were to sample enough data, we would start to see a
smooth curve when the mark ranges were narrowed to a
small difference (30-31, 31-32, etc)
A symmetrical frequency distribution graph with the same
mean, median and mode is called a normal distribution
(bell-shaped)
Note x is the symbol for mean and s (or )is the symbol for
standard deviation.
In a normal distribution, 68% of the numbers fall within 1
standard deviation of the mean, 95% are within 2 standard
deviations of the mean and 99% are within 3.
A bimodal distribution has two peaks, representing 2 modes
and is also symmetrical about the centres.
A skewed distribution is non-symmetrical.
Skewed
Bimodal
Text Problems: 3.6 from Homework Checklist Pg 153 #1-7
```
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