3-2 Notes

Measures of Variation

Simplest Measure of Variation is ______________. It gives the variation from the ____________ value to the ____________ value, but gives no indication of the variation for the rest of the data.

Ex. 1 Find the range of: 14, 15, 18, 20, 35

Standard Deviation – Gives you an idea of how data entries differ from _____________.Variance – Standard deviation ____________.

sample standard deviation:

sample variance:

Ex. 2 See Ex. 6 p. 89Hybrid A diameter (in.): 2 3 3 8 10 10

Use the defining formula to calculate the sample standard deviation

Step 1 Find the mean.Step 2 Find the sample variance

x

x23381010

xx 2xx

1

2

2

n

xxs

s =

Step 3 Find sample standard deviation

Hybrid B (GE #3 p. 89): 5 5 5 6 7 8 (use calc.)

Which hybrid would you use? Explain.

x s

Population variance and population standard deviation both divide by ____, not _________. Use if the data is the ___________________ and not just a ___________.

)( 2)(

Assignment p. 96 #1-4, 6-8, 9 d-e.

3-2 Notes Cont.

Measures of Variation

A disadvantage of the standard deviation as a comparative measure of variation is that it depends on _________________________. This means that it is difficult to use the standard deviation to compare measurements from ______________________. When we want to do this we use the ____________________ ____________, which expresses the standard deviation as ___________________________________.

Question: Is a $50 standard deviation large or small?

Jeans? Car?

CV = or

Ex. 1 Use the following sample data to determine which sports equipment has the greater relative variation.

Data 1 Sample prices of basketballs ($).11 12 9 10 10 9 9 5 18 14

Data 2 Sample prices of footballs ($).45 57 53 49 41 58 47 51 53 50

For Data 1 CV

For Data 2 CV

%100x

s

%100x

s

To find an interval in which a certain percentage of the data will definitely lie, we can use Chebyshev’s Theorem, which states:

For any set of data, the proportion of data that must lie within k standard deviations on either side of the mean is at least

Although this may make no sense to you ( ), the results ☺

of this theorem are as follows:For any set of data:

- At least 75% of the data will fall between - At least 88.9% of the data will fall between - At least 93.8% of the data will fall between

Ex. 2 Students Who Care is a student volunteer program in which college students donate work time in community centers for homeless people. For students in the program, the mean number of hours is hours each semester with a standard deviation hours. Find an interval A to B for the number of hours volunteered in which at least 75% of the students in this program would fit.

1.29x7.1s

TI Tips

To estimate mean and standard deviation of grouped data, enter the ____________ of the class into L1 and the _____________ of the class into L2. Then calculate 1-Var Stats linking L1 to L2.

Ex. 3 Based on data from USA Today, the ages of a random sample of 300 adults who shop by catalogue are

Estimate the mean, s.d., and the C.V. for this set of data.

Age 18-24

25-34

35-44

45-54

55-64

65 and up

Number

78 75 48 33 33 24use 69.5 for 65 and up midpoint

Assignment p. 98 #12 b-d, 13 b-d, 14, 15, 17, 18