aim: how do we organize and interpret statistical data?

Aim: Frequency Tables/Stem-Leaf/Histograms Course: Alg. 2 & Trig.

Do Now:

Aim: How do we organize and interpret statistical data?

Which task is not a component of an observational study?(1) The researcher decides who will make up the sample.(2) The researcher analyzes the data received from the sample.(3) The researcher gathers data from the sample, using surveys or taking measurements.(4) The researcher divides the sample into two groups, with one group acting as a control group.


Recall:

A teacher marked a set of 32 papers. The grades were as follows: 90, 85, 74, 86, 65, 62, 100, 95, 77, 82, 50, 83, 77, 93, 72, 98, 66, 45, 73, 100, 50, 89, 78, 70, 75, 95, 80, 78, 83, 81, 72, 75.

Find the significant statistical

measurements using the 1-var Stats option

on the graphing calculator.


Recall: Model Problem

A teacher marked a set of 32 papers. The grades were as follows: 90, 85, 74, 86, 65, 62, 100, 95, 77, 82, 50, 83, 77, 93, 72, 98, 66, 45, 73, 100, 50, 89, 78, 70, 75, 95, 80, 78, 83, 81, 72, 75.

STAT EDIT 1

STAT CALC 1 ENTER


Stem-and-Leaf Plots

Data - Test Scores: 90, 85, 74, 86, 65, 62, 100, 95, 77, 82, 50, 83, 77, 93, 72, 98, 66, 45, 73, 100, 50, 89, 78, 70, 75, 95, 80, 78, 83, 81, 72, 75

10 9 8 7 6 5 4

0002

1 52 3 3 6

5 5 = 55Key:

3 5 50 0

932 2 4 5 75 7 8 9

8

5 50 05

Stem Leaf

greatest stem to least

ordered leafs – lowest to highest


Stem-and-Leaf Plots

Data - John’s Test Scores: 67, 82, 86, 82, 85, 84, 85, 93, 73, 82

9 8 7 6

3237

67, 73, 82, 82, 82, 84, 84, 85, 85, 93

2 52 4 4 5

5 5 = 55Key:

Data - Marcia’s Test Scores: 66, 84, 86, 88, 88, 94, 95, 95, 98, 98

4

6

68 8 45588

put in order – lowest to highest


Stem-and-Leaf Plots

3rd type of graph representing data

3rd type of graph representing data

Data - John’s Test Scores: 67, 82, 86, 82, 85, 84, 85, 93, 73, 82 67, 73, 82, 82, 82, 84, 84, 85, 85, 93

9 8 7 6

3237

2 52 4 4 5

9 8 7 6

3 2 3 7

25

24

45

A stem-and-Leaf Plot rotated 1/4 turn

counterclockwise gives us a general outline

format for a histogram


Histogram/Bar Graph

A histogram is a bar graph that shows the frequency of occurrence

Frequency

80

70

60

50

40

30

20

10

051 - 60 61 - 70 71 - 80 81 - 90 91 - 100

Data Results

1. Horizontal axis - data organized in intervals 2. Vertical axis - the frequency of occurrence 3. For each interval, bar drawn to height of frequency 4. No space between bars


Model Problem

Recall our previous Paper Grade problem:

Recall our previous Paper Grade problem:

11

10

9

8

7

6

5

4

3

2

1

0

40-49 50-59 60-69 70-79 80-89 90-100

Frequency

Grades

Histogram of Paper Grades


TI Graphing

2ND Y= 1

Set WINDOW

GRAPH & TRACEuse right and left arrows to move thruintervals.


Model Problem11

10

9

8

7

6

5

4

3

2

1

0

41-50 51-60 61-70 71-80 81-90 91-100

Frequency

Grades

How many students scored better than 80?

How many students scored 70 or less?

A cumulative histogram makes it easier to answer such questions


Cumulative Historgram

33

30

27

24

21

18

15

12

9

6

3

0

41-50 51-60 61-70 71-80 81-90 91-100

Frequency

Grades

How many students scored better than 80?

How many students scored 70 or less?

Cumul at I ve

3 37

18

26

32

14

7

41-50 41-60 41-70 41-80 41-90 41-100


Cumulative Histogram33

30

27

24

21

18

15

12

9

6

3

0

41-50 51-60 61-70 71-80 81-90 91-100

Approximately what percent of students scored above 70?

Grades

3 37

18

26

32100%

75%

50%

25%

0%

Cu

mu

lati

ve F

req

uen

cy

Approximately What percent of students scored 100 or below?


Model Problems

11

10

9

8

7

6

5

4

3

2

1

0

16-19 20-23 24-27 28-31 32-35 36-39

Frequency

Answer the questions below based your interpretations of the histogram.

Mileage (miles per gallon) for compact cars

1) In what interval is the greatest frequency found? 2) What is the number of cars reporting mileages

between 28 and 31 miles? 3) What percent of cars reported mileages from 24 to 27 miles per gallon (to the nearest %)?


Model Problem

240 students took a math test. The frequency table below shows the results. Draw a histogram representing the results.

Interval TestScores

Frequency# Students

91 - 100 45

81 – 90 60

71 – 80 75

61 – 70 40

51 – 60 20

80

70

60

50

40

30

20

10

051 - 60 61 - 70 71 - 80 81 - 90 91 - 100

Test Scores

Frequency

What is the modal interval? 71-80

In what interval will you find the median?

Median is average of the 120th and 121st values. Both are located in the 71 - 80 interval.

aim: how do we organize and interpret statistical data?

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