w arm -u p. d ot p lots d efinition a data display in which each data item is shown as a dot above a...
TRANSCRIPT
WARM-UP
DOT PLOTS
DEFINITION
A data display in which each data item is shown as a dot above a number line
In a dot plot a cluster shows where a group of data points fall.
A gap is an interval where there are no data items.
HOW TO MAKE A DOT PLOT VIDEO
Creating a Dotplot
STEPS TO CREATE A DOT PLOT
1. Order numbers from least to greatest.2. Draw a number line.3. Label the number line with the minimum
and the maximum then all the numbers that fall between them.
4. Put a dot above each number on the number line for each data entry in your set.
5. Don’t forget a title and labels!
6
MAKING A DOT PLOT
I want to know more about my students who take Intro Stats so I’ve decided to take a survey and make a dot plot of the results
I’d like to find out about the pets they have in their household.
The question then becomes:
“How many pets are in your household?”
7MAKING A DOT PLOT FROM LIVE DATA
Frequency Frequency
0 pets 9 pets
1 pet 10 pets
2 pets 11 pets
3 pets 12 pets
4 pets 13 pets
5 pets 14 pets
6 pets 15 pets
7 pets 16 pets
8 pets 17 pets
8
DOT PLOT EXAMPLENumber of Pets Per Household
for Ms. H's Intro Stat Classes
2009
| | | | | | | | | | | | | | | | | | |
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Source: In Class Survey x-axis: # of Pets
Number of Pets Per Household for Ms. Watts’ Intro Stat Class 2014
9MAKING A DOT PLOT FROM LIVE DATA
Frequency Frequency
0 pets 9 pets
1 pet 10 pets
2 pets 11 pets
3 pets 12 pets
4 pets 13 pets
5 pets 14 pets
6 pets 15 pets
7 pets 16 pets
8 pets 17 pets
Relative Frequency
Relative Frequency
10
DOT PLOT: STATISTICAL VOCABULARY BACKGROUNDSpread (also called Variability)
The spread of data in statistics is the smallest value in a data set and the largest valueIt is always expressed as 2 numbersPrefer to write smallest then largest numberUnits are important
RangeThe range of data in statistics is the difference between the smallest value and the largest valueTake the spread and subtract the two numbers: large – smallUnits are important
11
DOT PLOT: STATISTICAL VOCABULARY BACKGROUND
One Measure of Center- MedianOne measure of the center of a data distribution is the median, the place where the data tends to be ½ above and ½ below.Units are important
ModeThe mode of data is a place or places with the largest number of data with the same value. Units are important.
12
DOT PLOT: HOW TO DESCRIBE ITShape
The shape of a data distribution possibilities:
1) SymmetrySymmetric Also ‘Fairly Symmetrical’Skewed Left (negatively skewed)Skewed Right (positively skewed)
2) PeaksSingle Peaked (unimodal)Double Peaked (bimodal)Multi Peaked (multimodal)
NOTE: Data have modes, dot plots have peaks
13
% OF POPULATION OVER 651 Alabama 13 26 Montana 13
2 Alaska 5 27 Nebraska 14
3 Arizona 13 28 Nevada 11
4 Arkansas 15 29 N Hampshire 12
5 California 11 30 N Jersey 14
6 Colorado 10 31 N Mexico 11
7 Connecticut 14 32 N York 13
8 Delaware 13 33 N Carolina 13
9 Florida 19 34 N Dakota 15
10 Georgia 10 35 Ohio 13
11 Hawaii 13 36 Oklahoma 14
12 Idaho 11 37 Oregon 14
13 Illinois 13 38 Penn 16
14 Indiana 13 39 R Island 16
15 Iowa 15 40 S Carolina 12
16 Kansas 14 41 S Dakota 14
17 Kentucky 13 42 Tennessee 13
18 Louisiana 11 43 Texas 10
19 Maine 14 44 Utah 9
20 Maryland 11 45 Vermont 12
21 Mass 14 46 Virginia 11
22 Michigan 12 47 Washington 12
23 Minnesota 12 48 W Virginia 15
24 Mississippi 12 49 Wisconsin 13
25 Missouri 14 50 Wyoming 11
14
POPULATION OVER 65 DATA SORTED BY %
1 Alaska 5 26 Indiana 13
2 Utah 9 27 Kentucky 13
3 Colorado 10 28 Alabama 13
4 Georgia 10 29 Montana 13
5 Texas 10 30 Arizona 13
6 N Mexico 11 31 Wisconsin 13
7 California 11 32 N York 13
8 Virginia 11 33 Ohio 13
9 Wyoming 11 34 Oklahoma 14
10 Maryland 11 35 Oregon 14
11 Idaho 11 36 Kansas 14
12 Louisiana 11 37 N Jersey 14
13 Nevada 11 38 Maine 14
14 Washington 12 39 Missouri 14
15 N Hampshire 12 40 Nebraska 14
16 S Carolina 12 41 Mass 14
17 Vermont 12 42 Connecticut 14
18 Mississippi 12 43 S Dakota 14
19 Michigan 12 44 Arkansas 15
20 Minnesota 12 45 N Dakota 15
21 Illinois 13 46 Iowa 15
22 N Carolina 13 47 W Virginia 15
23 Tennessee 13 48 R Island 16
24 Delaware 13 49 Penn 16
25 Hawaii 13 50 Florida 19
15
Make Dot Plot of State Population Data
Percent of Population over 65 years of Age
in the 50 States
.
:
: :
: . : :
: : : :
. : : : : :
. . : : : : : : : .
| | | | | | | | |
4 6 8 10 12 14 16 18 20
Source: Statistical Abstract of the US
x-axis: Number in % to nearest integer
16
DOT PLOT: HOW TO DESCRIBE ITMore on Shape
SymmetricWhen the left & right sides of a distribution are
mirror images of one anotherFairly Symmetric
When the left and right sides of a distribution are almost mirror images of one another, but there are small exceptions.Skewed Left (negatively skewed)
If a distribution extends much farther out to the left. The direction of skewness is on the side of
the longer tail, in this case LEFT.Skewed Right (positively skewed)
If a distribution extends much farther out to the right. The direction of skewness is on the side of
the longer tail, in this case RIGHT.
17
DOT PLOT: WHAT IT LOOKS LIKE
Shape: SymmetrySymmetric
18
DOT PLOT: WHAT IT LOOKS LIKE
More on Shape: Non SymmetricSkewed Left (negatively skewed)
Skewed Right (positively skewed)
Left Skew
Right Skew
tail
tail
19
TI83 AND SORT ASCENDING How to Sort Data in Ascending Order
Enter all values in a list at STAT EDITExit to Home Screen using 2nd MODEHit STAT key. Go to #2 SORT A(. Hit ENTERType 2nd 1 (if the data is in List 1). Hit EnterDone appearsCheck your data in List 1. It should be sorted.
Use your eyes to find the range & spread from the sorted list.
20
GOALS BY US WOMEN’S SOCCER
Number of Goals Scored by US Women's
Soccer Team in 34 games in 2004
3 0 2 7 8 2 4 4
5 1 1 4 5 3 1 1
3 3 2 1 2 2 2 4
6 6 1 5 5 1 1 4
3 3 Source: US Soccer Assn.
21
GOALS BY US WOMEN’S SOCCERORDERED ASCENDING
0 3 6
1 3 6
1 3 7
1 3 8
1 3
1 3
1 4
1 4
1 4
2 4
2 4
2 5
2 5
2 5
2 5
22
DOT PLOT OF GOALS BY US WOMEN’S SOCCERGoals per Game by US Women's Soccer Team in 2004
:
: : : .
: : : : :
. : : : : : : . .
| | | | | | | | | | |
0 1 2 3 4 5 6 7 8 9 10
Source: US Women's Soccer Assn
x-axis: # of goals per game
23
LIVING IN POVERTY EAST OF THE MISSISSIPPI
Percent of State Residents Living in Poverty
East of Mississippi River, 1999 Source: Stat Abs of US
Alabama 13 Maryland 6 Penn 8
Connecticut 6 Mass 7 Rhode Is 9
Delaware 7 Michigan 7 S Caroliina 11
Florida 9 Mississippi 16 Tennessee 10
Georgia 10 New Hamp 4 Vermont 6
Illinois 8 New Jersey 6 Virginia 7
Indiana 7 NY 12 W Virginia 14
Kentucky 13 N Carolina 9 Wisconsin 6
Maine 8 Ohio 8
24
LIVING IN POVERTY EAST OF THE MISSISSIPPIORDERED ASCENDING
New Hamp 4 Ohio 8
Wisconsin 6 Penn 8
Maryland 6 Rhode Is 9
Connecticut 6 Florida 9
New Jersey 6 N Carolina 9
Vermont 6 Georgia 10
Delaware 7 Tennessee 10
Indiana 7 S Caroliina 11
Mass 7 NY 12
Virginia 7 Alabama 13
Michigan 7 Kentucky 13
Illinois 8 W Virginia 14
Maine 8 Mississippi 16
25
LIVING IN POVERTY EAST OF THE MISSISSIPPI
% of State Residents Living in Poverty East of
the Mississippi River in 1999
. .
: : : .
. : : : : : . . : . .
| | | | | | | | | | | | |
4 5 6 7 8 9 10 11 12 13 14 15 16
Source: Statistical Abstract of the US
x-axis: Values to the nearest %
26
DOT PLOT: MEAN & MEDIAN ESSENTIALSSkew on a dot plot in relation to mean
and medianYou’ve drawn the line that connects the dot plot points on the top of the distribution. The line clearly shows right or left skew.If you have right skew, the mean will be to the right of (greater than) the median, as the mean follows the tail of the distribution.
Right Skew
meanmedian
tail
27
DOT PLOT: MEAN & MEDIAN ESSENTIALS
Skew on a dot plot in relation to mean and medianIf you have left skew, the mean will be to the left of (less than) the median, as the mean follows the tail of the distribution.
medianmean
Left Skewtail
28
DOT PLOT: DESCRIBING PEAKS
PeaksUnimodal
Bimodal
Unimodal
Bimodal
Multimodal (3 or more peaks)
Trimodalor Multimodal
29
DOT PLOT: TI ESSENTIALSFinding Mean and Median
Enter your data as a list in STAT EDITExit to home screen 2nd ModeGo to 2nd STAT.Right Arrow to MATH#3 is Mean; hit Enter; type 2nd and list #; Enter#4 is Median; hit Enter; type 2nd and list #;EnterCalculator does not give Mode. You need your eyes for that
30
DOT PLOT: HOW TO DESCRIBE ITUnusual Features. Possibilities include--
Potential Outliers: any data value that falls out of the pattern of the rest of the distribution. A potential outlier will lie at either extreme of the data when it is written in order. (We will learn how to calculate actual outliers later. For now, we will call these points potential outliers)Clusters: isolated groups of values. Clusters begin when frequency >1 and end before frequency returns to 1 or zero.
Gaps: large spaces between values. Write gap values from beginning empty space to end empty space. A gap of one number is NOT a gap.
31
FUEL CONSUMPTION—DATA
Fuel Consumption for 2009 Passenger Fords30 27 22 25 24 25 24 1535 35 33 49 49 10 27 1820 23 24 25 30 24 24 2418 20 25 27 24 32 29 2724 27 26 25 24 28 33 30
32
FUEL CONSUMPTION—DOT PLOT
Fuel Consumption for 2009 Passenger Fords
.:: . .: : : .
. . : : . . : : . : . . : . : : :
| | | | | | | | | | | | | | | | | | | | |
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50
Source: Consumer Reports x-axis: miles per gallon
YOU TRY IT! A. In an airline training program, the students
are given a test in which they are given a set of tasks and the time it takes them to complete the tasks is measured. The following is a list of the time (in seconds) for a group of new trainees.
61, 61, 64, 67, 70, 71, 71, 71, 72, 73, 74, 74, 75, 77,
79, 80, 81, 81, 83
Display the data in a dot plot.
ANSWER!
Airline Training Program TestNew Trainees
= 1 person
Time in Seconds
61
83
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
ARE THERE ANY CLUSTERS?
Airline Training Program TestNew Trainees
= 1 person
Time in Seconds
61
83
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
Yes!
ARE THERE ANY GAPS?Airline Training Program Test
New Trainees
= 1 person
Time in Seconds
61
83
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
Yes!
WHAT IS THE AVERAGE TIME?
Airline Training Program TestNew Trainees
= 1 person
Time in Seconds
61
83
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
About 73 seconds
WHAT IS THE MEDIAN TIME?
Airline Training Program TestNew Trainees
= 1 person
Time in Seconds
61
83
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
73 seconds
WHAT IS THE MODE? Airline Training Program Test
New Trainees
= 1 person
Time in Seconds
61
83
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
71 seconds
WHAT IS THE RANGE?
Airline Training Program TestNew Trainees
= 1 person
Time in Seconds
61
83
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
22 seconds
WHAT DOES THE MEDIAN REPRESENT?
Airline Training Program TestNew Trainees
= 1 person
Time in Seconds
61
83
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
The center of the data set.
WHAT DOES THE RANGE REPRESENT?
Airline Training Program TestNew Trainees
= 1 person
Time in Seconds
61
83
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
The variation in the data
set.
TRY AGAIN!
B. In a science class, the students weighed some samples of dirt to the nearest 1/8 pound. The weights of the samples are given below.
1/8 lb, 3/8 lb, ¾ lb, ¼ lb, 1/8 lb, ¼ lb, 7/8 lb, ¼ lb, 3/8 lb, ¼ lb, ½ lb, 3/8 lb
Make a dot plot for the data.
ANSWER!
Sample Weights
= 1 sample
Weight in pounds
0 18
28
38
48
58
68
78
1
ARE THERE ANY CLUSTERS?Sample Weights
= 1 sample
Weight in pounds
0 18
28
38
48
58
68
78
1
Yes!
ARE THERE ANY GAPS?Sample Weights
= 1 sample
Weight in pounds
0 18
28
38
48
58
68
78
1
Yes!
WHAT IS THE AVERAGE WEIGHT?
Sample Weights
= 1 sample
Weight in pounds
0 18
28
38
48
58
68
78
1
3/8 or 0.375 lb
WHAT IS THE MEDIAN?Sample Weights
= 1 sample
Weight in pounds
0 18
28
38
48
58
68
78
1
5/16 or 0.3125 lb
WHAT IS THE MODE?Sample Weights
= 1 sample
Weight in pounds
0 18
28
38
48
58
68
78
1
2/8 or 1/4 lb
WHAT IS THE RANGE?Sample Weights
= 1 sample
Weight in pounds
0 18
28
38
48
58
68
78
1
6/8 or 0.75 lb
WHAT DOES THE AVERAGE REPRESENT?
Sample Weights
= 1 sample
Weight in pounds
0 18
28
38
48
58
68
78
1
The center of the data set.
WHAT DOES THE RANGE REPRESENT?
Sample Weights
= 1 sample
Weight in pounds
0 18
28
38
48
58
68
78
1
The variation in the data set.
HOMEWORK