CHAPTER 2: MODELING DISTRIBUTIONS OF DATA

Section 2-1: Describing Location in a Distribution

Here is a random sample of 20 scores from the Chapter 1 Test:

61 68 72 75 75 77 78 78 79 80 80 80 80 81 81 83 88 91 95 99

Luke scored an 88. Find the percentile: ______

Percentile is the ______

Complete the following table:

Score Frequency Relative Frequency Cumulative Frequency Cumulative Relative Frequency

60-69

70-79

80-89

90-99

Make a cumulative relative frequency graph below:

Check for Understanding – Pg 89 #1 – 4

Definition: Standardized value (z-score)

If x is an observation from a distribution that has known mean and standard deviation, the standardized value of x is given by:

z =

A standardized value is often called a ______.

Here is some Minitab output from the Chapter 1 Test Scores:

Variable NMeanMedianStDevSE Mean

Test 1 scores858080104.33

Marty scored a 95 on the Chapter 1 Test. What is his standardized z-score? ______

Biff scored a 70 on the Chapter 1 Test. What is his standardized z-score? ______

Luke scored a 88 on the Chapter 1 Test. What is his standardized z-score? ______

Summarize in words the meaning of a z-score:______

______

Who in your AP Statistics class can be responsible for the z-score for the entire year? ______

Check for Understanding – Pg 91 #1 – 3

HOMEWORK: Pg 105 1, 5, 9, 11, 13, 15

There are two mathematical operations involved in calculating a z-score:

  1. First, we take each individual score, x, and ______the mean (remember the mean was 80). Fill in the table and then make a dotplot for each.

SCORE (x) SCORE (x) – MEANSCORE (x) SCORE (x) – MEAN

6180

6880

7280

7581

7581

7783

7888

7891

7995

8099

Dotplot for SCORE (x)Dotplot for SCORE (x) - MEAN

60 70 80 90 100 -20 -10 0 10 20

What happens to the shape, center, and spread for each distribution when you subtract the mean from each value? ______

  1. Second, we take the SCORE – MEAN and ______by the standard deviation (remember the standard deviation is 10). Fill in the table and then make a dotplot for each.

SCORE – MEAN SCORE – MEAN

Dotplot for SCORE - MEANDotplot for

.

-20 -10 0 10 20 -2 -1 0 1 2

What happens to the shape, center, and spread for each distribution when you divide by the standard deviation for each value? ______

Let’s summarize:

If you are given a list of data and you add or subtract the same value Q from each value. What will happen to the:

Shape:______

Center:______

Spread:______

If you are given a list of data and you multiply or divide by the same value W from each value. What will happen to the:

Shape:______

Center:______

Spread:______

So for our Chapter 1 Test Score data we started with a distribution that had a mean of _____ and a standard deviation of _____.

After we standardize all the values into z-scores, we end up with a distribution that has a mean of _____ and a standard deviation of _____.

Check for Understanding – Pg 97 #1 – 3

Strategy for exploring data:

  1. Start with a ______.
  2. Look for overall ______and striking ______such as outliers.
  3. Choose a numerical summary to describe ______and ______.

NEW! 4. Describe the pattern using ______.

Density curve has the following properties:

-- is always on or ______the horizontal axis.

-- has an area of _____ underneath the curve.

-- describes the overall pattern of a distribution.

-- it is an ______that is easy to use and ______enough

for practical use.

The area under the density curve for a certain range of values is equal to the ______of observations that fall in that range.

The ______is the equal areas point. Half of the data lies to the left of this value, and half to the right of it.

The ______is the balance point (average), at which point the curve would balance if made of solid material.

For a symmetric distribution, mean ____ median.

For a skewed left distribution, mean _____ median.

For a skewed right distribution, mean _____ median.

Check for Understanding – Pg 103 #1 – 4

  • HOMEWORK: Pg 107 19, 21, 23, 31, 33 - 38