Statistics Variance and
Standard Deviation
(using GDC)
(18FG)
1
Measures of Spread
If you selected a random data value from a set, how close to the mean would that data value likely be?
the variance and
standard deviation
tell us the answer
to this question
Example: The following data values represent the profit (in PhP) of a certain flower vendor in the Saturday Market. The data is taken for 8 Saturdays in a row.
7000 6000 8000 5000 4000 6000 7000 4000
a) Use your GDC to find the mean.
b) Use your GDC to find the standard deviation.
c) Explain the meaning of your answer to part b.
2
Variance and Standard Deviation
Variance and Standard Deviation make a lot more sense if you know how they are calculated.
Recall our "flower vendor profit" data:
7000 6000 8000 5000 4000 6000 7000 4000
If standard deviation is just the average difference of a data value from the mean, that should be easy to calculate, right?:
(mean = 5875)
data values
difference from the mean
(difference)2
4000
4000
5000
6000
6000
7000
7000
8000
3
Standard Deviation with Grouped Data
Example:
4
Standard Deviation of a Sample vs. Standard Deviation of a Population
Example:
unbiased estimate of the population standard deviation, given this data from a sample.
5
The Normal Curve
frequency
Many, many, many sets of data are distributed "normally" ­ they follow the pattern of the normal curve:
6
Why Standard Deviation is so, so cool
If data follows a normal distribution, the standard deviation of the data will always work like this:
What does this mean for our flower vendor?
7
Example:
8
Variance
Variance is the standard deviation squared.
The symbol for variance is _________.
9
Classwork/Homework:
18F (find variance too!) - #1-3, 10, 15
18G - #2, 3
10