aim: how do we organize and interpret statistical data?
DESCRIPTION
Aim: How do we organize and interpret statistical data?. Do Now:. 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. - PowerPoint PPT PresentationTRANSCRIPT
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.
Aim: Frequency Tables/Stem-Leaf/Histograms Course: Alg. 2 & Trig.
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.
Aim: Frequency Tables/Stem-Leaf/Histograms Course: Alg. 2 & Trig.
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
Aim: Frequency Tables/Stem-Leaf/Histograms Course: Alg. 2 & Trig.
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
Aim: Frequency Tables/Stem-Leaf/Histograms Course: Alg. 2 & Trig.
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
Aim: Frequency Tables/Stem-Leaf/Histograms Course: Alg. 2 & Trig.
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
Aim: Frequency Tables/Stem-Leaf/Histograms Course: Alg. 2 & Trig.
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
Aim: Frequency Tables/Stem-Leaf/Histograms Course: Alg. 2 & Trig.
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
Aim: Frequency Tables/Stem-Leaf/Histograms Course: Alg. 2 & Trig.
TI Graphing
2ND Y= 1
Set WINDOW
GRAPH & TRACEuse right and left arrows to move thruintervals.
Aim: Frequency Tables/Stem-Leaf/Histograms Course: Alg. 2 & Trig.
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
Aim: Frequency Tables/Stem-Leaf/Histograms Course: Alg. 2 & Trig.
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
Aim: Frequency Tables/Stem-Leaf/Histograms Course: Alg. 2 & Trig.
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?
Aim: Frequency Tables/Stem-Leaf/Histograms Course: Alg. 2 & Trig.
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 %)?
Aim: Frequency Tables/Stem-Leaf/Histograms Course: Alg. 2 & Trig.
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.