Homework Discussion

• Read pages 476 – 489

• Page 499: 1 – 3, 5, 7 – 11, 19, 21, (for 23, 25, 29, 30, 32, find the mean)

NUMERICAL SUMMARIES OF DATA (page 558)

Measures of location (central tendency) are numbers that tell us something about where the values of the data fall.

The average of a set of N numbers is obtained by adding the numbers and dividing by N.

Example. Average Home runs per season: Mike Sweeney

0

1

2

3

4

5

6

7

8

15 16 17 18 19 20 21 22 23

STEP 1. Calculate the total of the data.

)(...)()( 2211 nn fsfsfstotal STEP 2. Calculate N.

nfffN ...21

STEP 3. Calculate the Average. Average = total / N

THE AVERAGE (page 559).

Example 10. Starting Salaries of Philosophy Majors

Objective 1:

Creating examples and counterexamples

THE MEDIAN

FINDING THE MEDIAN OF N NUMBERS (page 563)

Step 1. Sort the original set.(Let represent the sorted data set.)}d,...,d,d,d{ N321

Step 2. Compute the value of the locator: L=N/2.

Step 3. The median is given by(a) if L is a whole number.

(b) if L is not a whole number.

21 LL dd

Ld

[Notation: is L rounded up]L

0

1

2

3

4

5

6

7

8

15 16 17 18 19 20 21 22 23

Frequency TableScore Frequency %

0 0 0.00%1 1 1.33%2 0 0.00%3 0 0.00%4 0 0.00%5 0 0.00%6 1 1.33%7 2 2.67%8 6 8.00%9 10 13.33%10 16 21.33%11 13 17.33%12 9 12.00%13 8 10.67%14 5 6.67%15 2 2.67%16 1 1.33%17 0 0.00%18 0 0.00%19 0 0.00%20 0 0.00%21 0 0.00%22 0 0.00%23 0 0.00%24 1 1.33%25 0 0.00%N= 75 100.00%

Frequency TableScore Frequency %

0 0 0.00%1 1 1.35%2 0 0.00%3 0 0.00%4 0 0.00%5 0 0.00%6 1 1.35%7 2 2.70%8 6 8.11%9 10 13.51%10 16 21.62%11 13 17.57%12 9 12.16%13 8 10.81%14 5 6.76%15 2 2.70%16 1 1.35%17 0 0.00%18 0 0.00%19 0 0.00%20 0 0.00%21 0 0.00%22 0 0.00%23 0 0.00%24 0 0.00%25 0 0.00%N= 74 100.00%

PERCENTILES (page 489)

The pth percentile of a data set is a value such that p percent of the numbers fall at or below the value and the rest fall at or above it.

FINDING THE PTH PERCENTILE OF N NUMBERS (page 561)

Step 1. Sort the original set.(Let represent the sorted data set.)}d,...,d,d,d{ N321

Step 2. Compute the value of the locator: L=(p/100)xN.

Step 3. The pth percentile is given by(a) if L is a whole number.

(b) if L is not a whole number.

21 LL dd

Ld

[Notation: is L rounded up]L

Example 12. Consider the GPAs of 15 students:3.4, 3.9, 3.3, 3.6, 3.5, 3.4, 4.0, 3.7, 3.3, 3.8, 3.6, 3.9, 3.7, 3.4, 3.6

3.3, 3.3, 3.4, 3.4, 3.4, 3.5, 3.6, 3.6, 3.6, 3.7, 3.7, 3.8, 3.9, 3.9, 4.0,

The 50th percentile of a data set is known as the median and is denoted by M.

The first quartile (denoted ) is the 25th percentile and the third quartile (denoted ) is the 75th percentile.

1Q

3Q

The median (50th percentile) is often called the second quartile.

THE QUARTILES (page 491)

0

1

2

3

4

5

6

7

8

15 16 17 18 19 20 21 22 23

Homework

• Read pages 487 – 495

• Page 499: 23, 25, 29, 30, 32, 33, 35, 37, 38, 41, 44, 45, 65, 67, 69

• There will be an exam on Tuesday 3/20