Download MBF3C 3.6 Common Distributions

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