Today’s Agenda

Attendance / AnnouncementsCollect Projects

Note about Final Exam

Return Exams

Remaining Schedule

Sections 10.1, 10.2

Exam Schedule

Exam 5 (Ch 10)

Thur 12/5

Final Exam (All)

Thur 12/12

Intro to Statistics

Statistics is the science that deals with the collection and summarization of data. Methods of stat analysis allow us to make conclusions about a population based on sampling.

Statistics is more a field of

Communications, than one of

Mathematics!

Intro to Statistics

1. Organize Data

2. Display Data

3. Identify the “averages” of the data

4. Identify the “spread” of the data

5. Make conclusions

Obtaining Data

• Want to represent a Population

• Collect data from a Sample

–Should be a Random Sample to be

a fair representation of the

population

Tuition for a random sample of 30

private, 4-year colleges(thousands)

23 22 38 25 11 16

15 26 23 24 37 18

21 36 36 28 18 9

39 17 27 24 10 32

24 27 22 24 28 39

23 22 38 25 11 16

15 26 23 24 37 18

21 36 36 28 18 9

39 17 27 24 10 32

24 27 22 24 28 39

There are 30 Data Items, so n = 30

Where each can be called

So,

“21”, “37”, etc. are Data Values

ix254x

Organizing Data

• Frequency Distribution Table– Organize data into Classes

• Usually between 5 - 15

– Each class must have the same Class Width

Class width* = Max data value – Min data value

Number of classes

*Round up to nearest integer

Organizing Data

Let’s make a Freq. Dist. Table with 7 classes to organize

the tuition data…Need Class Width!

28.47

939*CW

So, each class will have a class width of 5!

Organizing Data

Note: Class width is not (9 – 5)!!!

It is the distance between the lower

limit of each class.

Make

this

column

first!

Displaying Data1. An account ing firm selected 24 complex tax returns prepared by a certa in tax preparer. The number of

errors per return were as follows. Group the data into 5 classes, and make a frequency table and

histogram/ polygon to represent the data.

Your Class Width =

8 12 0 6 10 8 0 14

8 12 14 16 4 14 7 11

9 12 7 15 11 21 22 19

Displaying Data

• Frequency Histogram (bar graph)–Each class is its own “bar”

• No spaces between classes (bars)

–Must label each axis (classes vs. frequency)

–Use straightedge to make lines

1

3

4

5

6

7

8

9

2

freq

uen

cy

Tuition

5-9

10

-14

15-1

9

20

-24

25-2

9

30-3

4

35-3

9

Displaying Data

• Frequency Polygon (line graph)

–Connects the midpoints of the top of each class.

–Then connect to ground on each side

–Use straightedge to make lines

1

3

4

5

6

7

8

9

2

freq

uen

cy

Tuition

5-9

10

-14

15-1

9

20

-24

25-2

9

30-3

4

35-3

9

Characterizing Data

Displaying Data1. An account ing firm selected 24 complex tax returns prepared by a certa in tax preparer. The number of

errors per return were as follows. Group the data into 5 classes, and make a frequency table and

histogram/ polygon to represent the data.

Your Class Width =

8 12 0 6 10 8 0 14

8 12 14 16 4 14 7 11

9 12 7 15 11 21 22 19

10.2 Measures of Central Tendency

• Ways to describe “on average…”

–Mean

• What is commonly thought of as

“average”

–Median

• The “middle” of the data

–Mode

• The data value that occurs most often

We need some data…

• Number of hits during spring training for 15

Phillies players: (alphabetical order)

21 19 10 1 6

28 32 11 2 15

2 17 21 29 21

Sample Mean

n

xx

• The mean of a sample set of data

“x bar” is the

sample mean.

Round to

nearest

hundredth. (2

decimal places)

The sum of all

data values

The number of

data items

• Number of hits for 15 Phillies players:

21 19 10 1 6

28 32 11 2 15

2 17 21 29 21

67.1515

211921

n

xx

Median

• The “middle” of an ordered data set

– Arrange data in order

– Find middle value

• If n is odd, simply select middle value as the

median.

• If n is even, the median value will be the

mean of the two central values (since a

“middle” does not exist)

2

1nposition

Median

Find the median for each data set.

Age (years) in the intensive care unit at a local hospital.

68, 64, 3, 68, 70, 72, 72, 68

Starting teaching salaries (U.S. dollars).

$38,400, $39,720, $28,458, $29,679, $33,679

Median

• When is median a better indicator of

“average” than the mean?

Mode

• The data value that appears most often

– Single Mode

• One data value appears more than any other

– No Mode

• No data values repeat

– Multi-Mode

• There is a “tie” for the value that appears the most

Mode

• Mode of Phillies data?

• 2, 3, 3, 3, 5, 6, 6, 6, 7, 7, 10

• 18, 34, 61, 62, 85

• 9.5, 9.2, 9, 9, 9.1, 8.9

Classwork / Homework

• Page 604

•1, 7, 21 – 25

• Page 614

•1 – 19 odd, 29