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Standard Deviation
Normal Distribution
Normal Distribution
A common type of distribution where more
values are closer to the mean, and as you
move away from the mean, there are less
data.
Normal Distribution
The more data
collected the
histogram will start to
form a very distinct
shape.
The Bell Curve
The distribution will
be very bell shaped.
The Bell Curve
Very specific percentages of the area
are located within one and two
standard deviations of the mean.
Percentages
About 68% of the data will lie within one
standard deviation from the mean.
M ± SD (Likely that data will lie in this interval)
About 95% of the data will lie within two
standard deviations from the mean.
M ± 2SD (Very likely that data will lie in this
interval)
Considered Not Likely that data will lie outside
the 95%.
Example 1
Suppose the number of songs on students
iPods was recorded and the mean was
160 with a standard deviation of 35.
68% of the students should have songs
between what values?
95% of the students should have songs
between what values?
Example 2
There are 240 smokers at PA. A sample
was taken and the mean number of
smokes per day was 12 with a standard
deviation of 3.
What percentage of students smoke
between 6 and 18 smokes per day.
Using the sample, how many students
would you expect to smoke between 9 and
15 smokes per day?
Significant Differences
If a piece of data lies within 95% of the
data we say that this is not a significant
difference from the mean.
If it lies outside the 95%, this is considered
to be a significant difference.
Significant Difference - Example
Paula checks three samples of wheel
bearings. The first is assumed to have a
mean lifetime of 2000 h and a standard
deviation of 400 h. The second and third
boxes are unlabelled.
She selects an item from each box
The sample from box 2 fails after 1300 h.
The sample from box 3 fails after 2900 h.
Is either of the findings significant?
Confidence Intervals
We can accurately say that the population
mean is within 95% of the sample mean.
Confidence Intervals
Example:
Dana conducted a survey on how much
money students typically spend per week
on lunch. His sample of 40 randomly
chosen students gave a mean of $15.25.
Dana knows that the standard deviation is
$2.00. What is the population mean.
Confidence Intervals
Example:
$15.25 + 2($2.00) = $19.25
$15.25 – 2($2.00) = $11.25
Dana can be 95% confident that the
population mean is between $11.25 and
$19.25.