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Seminar 9:

Statistics, Part II

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Measures of Central Tendency

Measures of Central Tendency section 9.1

The mean of a set of numbers is the average.

Example: 12, 5, 7, 16

mean = (12+5+7+16)/4 = 10

Measures of Central Tendency section 9.1

Example: The mean of five test scores is 81.

What is the sum of the test scores?

Measures of Central Tendency section 9.1

page 368 #37

Measures of Central Tendency section 9.1

The median of a set of numbers is the middle number.

Example: 5, 3, 11, 9, 8, 15, 2

Order the numbers: 2,3,5,8,9,11,15

The median is the middle number = 8

Measures of Central Tendency section 9.1

If there are an even number of values:

Example: 5, 3, 11, 9, 8, 15, 2, 20

Order the numbers: 2,3,5,8,9,11,15, 20

The median is the average of the

middle numbers = (8+9)/2 = 8.5

Measures of Central Tendency section 9.1

Mode = most frequently occurring value (may have more

than one mode)

ex: 1,1,2,2,2,5,7,8,8,8,9

Midrange = (low val + high val) / 2

Measures of Central Tendency section 9.1

Values: 2 3 7 9 10 13 17 21 22 25 30

Median = "50th percentile" = Q2

First Quartile = median of lower half = Q1

Third Quartile = median of upper half = Q3

Measures of Central Tendency section 9.1

Values:

15 19 19 20 22 23 24

24 24 25 26 27 29 30

32 34 34 35 36 39 42

What are Q1 , Q2 and Q3 ?

Measures of Central Tendency section 9.1

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Measures of Dispersion

Measures of Dispersion section 9.2

Two data sets with mean = 50

Data Set 1: 48, 49, 50, 51, 52

Data Set 2: 10, 20, 50, 80, 90

What is the difference?

Measures of Dispersion section 9.2

Range = high val - low val

Example: 11, 9, 6, 12, 17

What is the range?

Measures of Dispersion section 9.2

Standard Deviation: "average" deviation from the mean

Data Set: 2, 3, 5, 8, 9, 11, 18

The Normal Curve

The Normal Curve section 9.3

Data which approximates a Normal Distribution

The Normal Curve section 9.3

The Normal Curve section 9.3

Use table 9.4 to find the area to the right of z = 1.34

The Normal Curve section 9.3

Use table 9.4 to find the area to the left of z = 1.62

The Normal Curve section 9.3

Use table 9.4 to find the area between z = -1.32 and

z = -1.64

The Normal Curve section 9.3

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The Normal Curve section 9.3

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The Normal Curve section 9.3

Assume that math SAT scores are normally distributed with

a mean of 500 and a standard deviation of 100.

What percent of students who took the test have a math

score below 550?

The Normal Curve section 9.3

Assume that math SAT scores are normally distributed with

a mean of 500 and a standard deviation of 100.

What percent of students who took the test have a math

score above 650?

The Normal Curve section 9.3

Assume that math SAT scores are normally distributed with

a mean of 500 and a standard deviation of 100.

What percent of students who took the test have a math

score between 550 and 650?

Linear Regression