Measures of Spread

​MEASURES OF SPREAD
3.2

​COLEGIO INTERNACIONAL DE CARABOBO
SECONDARY MATH DEPARTMENT
STATISTICS

​WHAT WE WILL LEARN TODAY...

• Range

• Population Variance and Population Standard Deviation.

• Sample Variance and Sample Standard Deviation

• Variance and Standard Deviation for Grouped Data

• Coefficient of Variation

• Range Rule of Thumb

• Chebyshev’s Theorem

• The Empirical (Normal) Rule

BEFORE WE START!

What are measures
of Spread?

BEFORE WE START!

What are measures
of Spread?

​

Range

Population Variance and Population Standard Deviation.

Sample Variance and Sample Standard Deviation

Variance and Standard Deviation for Grouped Data

Coefficient of Variation

Range Rule of Thumb

Chebyshev’s Theorem

The Empirical (Normal) Rule

​Measures of Spread

​RANGE

​The range is the highest value minus the lowest value. The symbol R is used for the range.

R = highest value - lowest value

Multiple Choice

What is the range of Paint A and B?

• 60 and 45

• 10 and 25

• 50 and 20

• 50 and 45

​

Range

Population Variance and Population Standard Deviation.

Sample Variance and Sample Standard Deviation

Variance and Standard Deviation for Grouped Data

Coefficient of Variation

Range Rule of Thumb

Chebyshev’s Theorem

The Empirical (Normal) Rule

​Measures of Spread

​POPULATION VARIANCE AND SD

​

Range

Population Variance and Population Standard Deviation.

Sample Variance and Sample Standard Deviation

Variance and Standard Deviation for Grouped Data

Coefficient of Variation

Range Rule of Thumb

Chebyshev’s Theorem

The Empirical (Normal) Rule

​Measures of Spread

​POPULATION VARIANCE AND SD

​

Range

Population Variance and Population Standard Deviation.

Sample Variance and Sample Standard Deviation

Variance and Standard Deviation for Grouped Data

Coefficient of Variation

Range Rule of Thumb

Chebyshev’s Theorem

The Empirical (Normal) Rule

​Measures of Spread

​POPULATION VARIANCE AND SD

Multiple Choice

Find the variance and standard deviation for brand B paint data in Example 3–15.

The months brand B lasted before fading were 35, 45, 30, 35, 40, 25

• $$\sigma^2\ =\ 5.6\ \ \ \sigma=39.7$$

• $$\sigma^2\ =6.5\ \ \ \sigma=41.7$$

• $$\sigma^2\ =\ 39.7\ \ \ \sigma=5.6$$

• $$\sigma^2\ =\ 41.7\ \ \ \sigma=6.5$$

​

Range

Population Variance and Standard Deviation.

Sample Variance and Standard Deviation

Variance and Standard Deviation for Grouped Data

Coefficient of Variation

Range Rule of Thumb

Chebyshev’s Theorem

The Empirical (Normal) Rule

​Measures of Spread

​SAMPLE VARIANCE AND SD

Multiple Choice

How do I calculate the Standard Deviation from a Sample?

• I square root it

• I raise it to the square

• I divided it by two

• I get the product of that and 2

​

Range

Population Variance and Standard Deviation.

Sample Variance and Standard Deviation

Variance and Standard Deviation for Grouped Data

Coefficient of Variation

Range Rule of Thumb

Chebyshev’s Theorem

The Empirical (Normal) Rule

​Measures of Spread

​SAMPLE VARIANCE AND SD

​

Range

Population Variance and Standard Deviation.

Sample Variance and Standard Deviation

Variance and Standard Deviation for Grouped Data

Coefficient of Variation

Range Rule of Thumb

Chebyshev’s Theorem

The Empirical (Normal) Rule

​Measures of Spread

​SAMPLE VARIANCE AND SD

Multiple Choice

Teacher Strikes

The number of public school teacher strikes in Pennsylvania for a random sample of school years is shown. Find the sample variance and the sample standard deviation.

2 1 11 6 5 9

• $$s^2\ \approx\ 15.07\ \ \ s\approx3.89$$

• $$s^2\ \approx\ 3.89\ \ \ s\approx15.07$$

• $$s^2\ \approx\ 17.05\ \ \ s\approx3.98$$

• $$s^2\ \approx\ 3.98\ \ s\approx17.05$$

​

Range

Population Variance and Standard Deviation.

Sample Variance and Standard Deviation

Variance and Standard Deviation for Grouped Data

Coefficient of Variation

Range Rule of Thumb

Chebyshev’s Theorem

The Empirical (Normal) Rule

​Measures of Spread

VARIANCE AND SD FOR GROUPED DATA

​

Range

Population Variance and Standard Deviation.

Sample Variance and Standard Deviation

Variance and Standard Deviation for Grouped Data

Coefficient of Variation

Range Rule of Thumb

Chebyshev’s Theorem

The Empirical (Normal) Rule

​Measures of Spread

VARIANCE AND SD FOR GROUPED DATA

​

Range

Population Variance and Standard Deviation.

Sample Variance and Standard Deviation

Variance and Standard Deviation for Grouped Data

Coefficient of Variation

Range Rule of Thumb

Chebyshev’s Theorem

The Empirical (Normal) Rule

​Measures of Spread

VARIANCE AND SD FOR GROUPED DATA

​

Range

Population Variance and Standard Deviation.

Sample Variance and Standard Deviation

Variance and Standard Deviation for Grouped Data

Coefficient of Variation

Range Rule of Thumb

Chebyshev’s Theorem

The Empirical (Normal) Rule

​Measures of Spread

VARIANCE AND SD FOR GROUPED DATA

​

Range

Population Variance and Standard Deviation.

Sample Variance and Standard Deviation

Variance and Standard Deviation for Grouped Data

Coefficient of Variation

Range Rule of Thumb

Chebyshev’s Theorem

The Empirical (Normal) Rule

​Measures of Spread

VARIANCE AND SD FOR GROUPED DATA

Multiple Choice

Cost per Load of Laundry

Detergents The costs per load (in cents) of 35 laundry detergents tested by a consumer organization are shown here. Find the variance and standard deviation for the data.

• s² =125.96

  s= 11.22

• s²= 275.26

  s=15.32

• s² = 425.21

  s = 24.15

• s² = 124.57

  s=11.75

Poll

Do we make the rest of the classes like this?

(was this effective in your learning process)

• YES

• NO