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TRANSCRIPT
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Table of Contents
Data DisplaysFrequency Tables and HistogramsBox-and-Whisker Plots
Click on a topic to go to that section.
Dot PlotsAnalyzing Data DisplaysGlossary & Standards
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TablesTicket Sales for School Play
ChartsGraphs
Friday Saturday Sunday
7 PM 78 67 65
9 PM 82 70 30
Matinee NA 35 82
Data Display Example
Teac
her N
otes
&
Mat
h Pr
actic
e
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A frequency table shows the number of times each data item appears in an interval.
To create a frequency table, choose a scale that includes all of the numbers in the data set.
The table should have the intervals in the first column, tally in the second and frequency in the third.
Time Tally Frequency10-19 IIII 420-29 0 30-39 IIII 540-49 IIII 450-59 060-69 III 3
Frequency Table
Next, determine an interval to separate the scale into equal parts.
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The following are the test grades from a previous year.Organize the data into a frequency table.
95 85 9377 97 7184 63 8739 88 8971 79 8382 85
Frequency Table Practice
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95 85 9377 97 7184 63 8739 88 8971 79 8382 85
Step 1: Find the range of the data then determine a scale and interval.Hint: Divide the range of data by the number of intervals you would like to have and then use the quotient as an approximate interval size.
RANGE:
SCALE:
INTERVALS:
Range, Scale, and Interval
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95 85 9377 97 7184 63 8739 88 8971 79 8382 85
Grade Tally Frequency
Test Grades
Create a Frequency Table
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Length of Time Walking 15 30 15 45 45 30 30 60 30 60 15 30 45 45 60 15
Create a Frequency Table
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A histogram is a bar graph that shows data in intervals. It is used to show continuous data.
Since the data is shown in intervals, there is no space between the bars.
FREQUENCY
8
6
4
2
030- 40- 50- 60- 70- 80- 90-39 49 59 69 79 89 99
GRADE
Test Grades
Histogram
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Grade Tally Frequency30-39 I 140-49 050-59 060-69 I 170-79 IIII 480-89 IIII III 890-99 III 3
Test Grades
95 85 9377 97 7184 63 8739 88 8971 79 8382 85
FREQUENCY
8
6
4
2
030- 40- 50- 60- 70- 80- 90-39 49 59 69 79 89 99
GRADE
Test Grades
Note: Frequency tables and histograms show data in intervals
Create a Histogram
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Que
stio
ns
FREQUENCY
8
6
4
2
030- 40- 50- 60- 70- 80- 90- 39 49 59 69 79 89 99
GRADE
Test Grades
1. How many students scored an A?2. How many students scored an 87?3. How are histograms and bar graphs alike?4. How are histograms and bar graphs different?5. Why are there no spaces between the bars of a histogram?
Histogram Questions
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Notice that the test scores are closely grouped except one.
In statistics when a value is much different than the restof the data set it is called an outlier.
Que
stio
ns
FREQUENCY
8
6
4
2
030- 40- 50- 60- 70- 80- 90- 39 49 59 69 79 89 99
GRADE
Test Grades
Histogram
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Grade Tally Frequency30-39 I 140-49 050-59 060-69 I 170-79 IIII 480-89 IIII III 890-99 III 3
TEST SCORES95 85 9377 97 7184 63 8739 88 8971 79 8382 85
EXAMPLE:
Que
stio
nsFREQUENCY
8
6
4
2
0 30- 40- 50- 60- 70- 80- 90-39 49 59 69 79 89 99
GRADE
Test Grades
Histogram Example
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Create a Frequency Table & Histogram for the following data:
TEST SCORES 87 53 95 85 89 59 86 82 87 40 90 72 48 68 57 64 85
FREQUENCY
8
6
4
2
0 30- 40- 50- 60- 70- 80- 90-39 49 59 69 79 89 99
GRADE
Test Grades
Histogram Practice
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Bar Graphs and Histograms
Both compare data in different categories and use bars to show amounts.
Histograms show data in intervals, the height of the bar shows the frequency in the interval and there are no spaces between the bars.Bar Graphs show a specific value for a specific category, and have a space between bars to separate the categories.
FREQUENCY
8
6
4
2
0 30- 40- 50- 60- 70- 80- 90-39 49 59 69 79 89 99
GRADE
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This table shows the ages of 20 visitors at a library.
Create a histogram (on the next page) that represents the data. Adjust the size of the slider by dragging the top of the slider to the appropriate height.
From PARCC EOY sample test non-calculator #10
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A box and whisker plot is a data display that organizes data into four groups.
10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10 80 90 100 110 120 130 140 150
The median divides the data into an upper and lower half
The median of the lower half is the lower quartile.
The median of the upper half is the upper quartile.
The least data value is the minimum.
The greatest data value is the maximum.
Box and Whisker Plot
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10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10 80 90 100 110 120 130 140 150
Drag the terms below to the correct position on the box and whisker graph.
median lower quartile upper quartile
minimummaximum
Box and Whisker Plot
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10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10 80 90 100 110 120 130 140 150
median
25% 25%25%25%
The entire box represents 50% of the data. 25% of the data lie in the box on each side of the median
Each whisker represents 25% of the data
Box and Whisker Plot
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1 The minimum is
A 87B 104C 122D 134
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2 The median is
A 87B 104C 122
D 134
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3 The lower quartile is
A 87B 104C 122D 134
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4 The upper quartile is
A 87B 104C 122D 134
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5 In a box and whisker plot, 75% of the data is between
A the minimum and medianB the minimum and maximumC the lower quartile and maximum
D the minimum and the upper quartile
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6 In a box and whisker plot, 50% of the data is between
A the minimum and medianB the minimum and maximumC the lower quartile and upper quartileD the median and maximum
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7 In a box and whisker plot, 100% of the data is between
A the minimum and medianB the minimum and maximumC the lower quartile and upper quartileD the median and maximum
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Find the following:
· Minimum· Lower Quartile· Median· Upper Quartile· Maximum
Steps for creating a box and whisker plot:
88 96 96 97 101 105 105 107 111 112115 119 122 122 122 124 125 128 129 132133 136 138 139 139 147 148
Creating a Box and Whisker Plot
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Create a box and whisker plot by plotting all 5 pieces of information. Then draw the plot.
Minimum = 88Lower Quartile = 105Median = 122Upper Quartile = 133Maximum = 148
10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10 80 90 100 110 120 130 140 150
Creating a Box and Whisker Plot
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8
True
Compare the two box and whisker plots.
Wrestling Team Weights
10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10 80 90 100 110 120 130 140 150
Last year
This year
The interquartile range for last year's team was 15.
10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10 80 90 100 110 120 130 140 150
False
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9
True
Compare the two box and whisker plots.
Wrestling Team Weights
10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10 80 90 100 110 120 130 140 150
Last year
This year
The interquartile range for last year's team was 15.
10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10 80 90 100 110 120 130 140 150
False
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10
True
Compare the two box and whisker plots.
Wrestling Team Weights
10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10 80 90 100 110 120 130 140 150
Last year
This year
Both teams have about the same range.
10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10 80 90 100 110 120 130 140 150
False
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11
True
Compare the two box and whisker plots.
Wrestling Team Weights
10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10 80 90 100 110 120 130 140 150
Last year
This year
Last year's quartiles and median are lower than this year's.
10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10 80 90 100 110 120 130 140 150
False
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12
True
Compare the two box and whisker plots.
Wrestling Team Weights
10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10 80 90 100 110 120 130 140 150
Last year
This year
50% of the wrestlers weighed between 110 and 140 last year.
10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10 80 90 100 110 120 130 140 150
False
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10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10
Try this!
Minimum = _____________Lower Quartile = ___________ Median = ______________Upper Quartile = __________Maximum = _______________
26 26 26 28 29 35 36 37 38 3940 40 41 41 41 42 43 44 45 4850 52 53 53 55 56 57 61 62 6364 67 70 73
Box and Whisker Plot Practice
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10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10
Minimum = _____________Lower Quartile = ____________Median = _____________Upper Quartile = ____________ Maximum = _____________
Try this!
107 115 116 129 132 134 140 142 142 144145 148 149 152 153 154 154 154 154 155
Box and Whisker Plot Practice
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A dot plot (line plot) is a number line with marks that show the frequency of data. A dot plot helps you see where data cluster.
Example:
35 40 45 5030
xxxxxx
xxx
xxx
xxxx
xx
xxx
xxxxx
Test Scores
The count of "x" marks above each score represents the number of students who received that score.
Dot Plot
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Use the dot plot to answer the following questions.
How many students took the test?What is the minimum score? Maximum?What is the mean?What is the mode?What is the median (Q2)?What is the lower quartile? Upper quartile?
35 40 45 5030
xxxxxx
xxx
xxx
xxxx
xx
xxx
xxxxx
Test Scores
Dot Plot
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How to Make a Dot Plot
1. Organize the data. Use a list or frequency table.
2. Draw a number line with an appropriate scale.
3. Count the frequency of the first number and mark the same amount of x's above that number on the line.
4. Repeat step 3 until you complete the data set.
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1. Organize the data. Use a list or frequency table.
Miley is training for a bike-a-thon. The table shows the number of miles she biked each day. She has one day left in her training. How many miles is she most likely to bike on the last day?
4 2 9 3 3
5 5 1 6 2
5 2 4 5 5
9 4 3 2 4
Distance Miley Biked (mi)Miles Frequency
1 1
2 4
3 3
4 4
5 5
6 1
9 2
How to Make a Dot Plot
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2. Draw a number line with an appropriate scale.
1 2 3 4 5 6 7 8 9 10
3. Count the frequency of the first number and mark the same amount of x's above that number on the line.
4. Repeat step 3 until you complete the data set.
How many miles is Miley most likely to bike on her last day?
How to Make a Dot Plot
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Ms. Ruiz made a line plot to show the scores her students got on a test. Below is Ms. Ruiz's dot plot.
Use the dot plot to answer the next few questions.
75 80 85 90 95 100
xxxxxx
xxxxx
xxxxx
xxxxxx
xxx
xxxx
Test Scores
Dot Plot Practice
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13 What does each data item or "x" represent?
A the teacherB a studentC the test scoreD the entire class
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14 How many more students scored 75 than scored 85?
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15 What is the median score?
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16 What is the lower quartile of the test scores?
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17 The upper quartile is 90.
True
False
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18 What percent of the students scored an 80 or above on the test?
A 25%B 50%C 75%D 100%
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19 What is the interquartile range of the test scores?
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20 What is the mean of the test scores?
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21 What are the mode(s) of the data set?
A 75B 80C 85D 90E 95F 100
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22 The adults of a certain type of insect have a mean length of 0.6 inch. The students in a science class measured 10 insects of this type. The lengths are shown in the line plot.
Part A How many of the insects have a length that is greater than 0.6 inch?
insects
From PARCC EOY sample test calculator #13
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23 Part B
Select one answer from each group to correctly complete the sentence. The mean of the lengths of the insects measured by the science class is __________, which is _________ than the mean length of adults of that type of insect.
A 3/8
B 1/2
C 5/8
D 3/4
From PARCC EOY sample test calculator #13
E greater
F less
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Try This!
Doug kept a record of how long he studied every night. Create a dot plot using the following data.
30 60 30 90
90 60 120 30
60 120 60 60
120 30 120 60
Doug's Study Times (minutes)
Data Plot Practice
Ans
wer
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A data display shows us a lot of information about the measures of center
Find the:
Mean _____Median _____Mode _____Range _____
Analyzing Data Displays
and variability.
We can also determine a lot about the data that was collected by looking at a data display.
Let's look at the most recent test scores of some 6th grade students.
45 53 56 60 62 70 70 70 74 8383 83 85 85 88 91 91 95 98 98
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The mean and median are not very close in this problem.
The mode is not the best choice to describe a data set because there can be more than one mode.
The range only tells us what the difference is but does not tell us how well most of the students performed on the test.
FREQUENCY
8
6
4
2
030- 40- 50- 60- 70- 80- 90- 39 49 59 69 79 89 99
GRADE
Test Grades
Notice that the histogram is not symmetrical. The data is pulled to the left because some students scored low.
MedianMean
Analyzing Histograms
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After the test, some students decided to re-take the test to improve their grade. The following are the new scores.
68 69 70 70 70 74 76 81 82 8383 83 85 85 88 91 91 95 98 98
The new mean is 82 and very close to the median which is 83.
FREQUENCY
8
6
4
2
0 30- 40- 50- 60- 70- 80- 90- 39 49 59 69 79 89 99
GRADE
Test GradesNotice that the histogram is more symmetrical. The data is more symmetrically distributed because the scores are closer together.
Mean & Median
Analyzing Histograms
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Time Spent Doing Homework Last Night (Min)
0 5 10 15 20 25 30 35 40 45 50
The box and whisker plot above shows the number of minutes students spent doing homework last night.
The median is closer to the minimum than the maximum.
This means that 50% of the students that spent under 25 minutes on their homework probably spent a similar amount of time to each other.
On the other hand, the other half that studied more than the median time probably spent very different lengths of time on their homework.
Analyzing Box and Whisker Plots
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Time Spent Doing Homework Last Night (Min)
0 5 10 15 20 25 30 35 40 45 50Q1 Q3
The difference of the lower quartile and minimum is 5.
This shows us that 25% of the students shared a similar amount of studying time that was less than 20 minutes. The data is concentrated.
The difference of the maximum and upper quartile is 10.
This shows us that those students spent very different amounts of time so the "whisker" is longer even though it represents 25% of the class.
Analyzing Box and Whisker Plots
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Students are asked to record the number of hours they volunteer doing community service per week.
0 1 2 3 4 5 6 7 8 9 10
xxx
xxxx x x
xxxxx
xxx x
xx
Community Service
Number of Hours per WeekFind the:
Mean _____Median _____Mode _____Range _____
Analyzing Dot Plots
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0 1 2 3 4 5 6 7 8 9 10
xxx
xxxx x x
xxxxx
xxx x
xx
Community Service
Number of Hours per Week
Does the dot plot look symmetrically distributed?Why is the mean closer to 4 than to 3?
Analyzing Dot Plots
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24 The median is greater than the mean. Explain your answer. (Determine by analyzing the graph instead of using a calculator.)
True
False
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25 Which measure of center appropriately represents the data?
A MeanB Median
Paper Plane Competition
Distance (ft)
FREQUENCY
4
3
2
1
0 0-4 5-9 10-14 15-19 20-24
C Mode
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26 The number that is represented by the smallest interval on this histogram is called the ______________.
Paper Plane Competition
Distance (ft)
FREQUENCY
4
3
2
1
0 0-4 5-9 10-14 15-19 20-24
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27 The students in the older half of the group are
A very close in ageB not so close in ageC cannot be determined
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28 In which interval are the students closest in age to each other?
A 130 - 132.5B 132.5 - 139C 139 - 142.5
D 142.5 - 150
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Back to
Instruction
Box and Whisker Plot
A diagram or graph that uses a number line to show the distribution of a set of data.
1 2 3 4 5 6 7 8
Q1 Q2 Q3
+
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Back to
Instruction
ConcentratedWhen there is a high frequency of a value relative to the other values in a set of data.
High
+ + +
Concentration
+
LowConcentration
of juice of juice
100% Concentration
of water
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2
4
6
8
DistributionThe variation and frequency of
each value in a set of data.
redbrown
yellowgreenblueorange
773311
Back to
Instruction
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Back to
Instruction
Dot PlotA graph that uses a number line to show the
frequency of each value in a set of data.
1 2 3 4 5 6 7 83,4,6,2, 4,1,8,4,3
# of People in Family
1 2 3 4 5 6 7 8
x xxx
xxxx
x x
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Back to
Instruction
Frequency TableA chart of columns and rows, used to record the values in a data set and how often each
value occurs.
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Back to
Instruction
HistogramA bar graph representing the frequency of
data for certain ranges or intervals.
Scores:63,65,67,70,72,74, 75,75,75,78,79,80, 80,82,82,85,85,85, 85,87,89,92,94,94, 95,96,98,100,100,
100
60-6970-7980-8990+
38109
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Back to
Instruction
IntervalThe equal number of units
between each number on a scale.
0, 5, 10, 15...
Interval of 5
Interval of 2
0, 2, 4, 6, 8...
Interval of 100
0, 100, 200...
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Back to
Instruction
Measures of CenterStatistics used to describe the "center" of the
distribution of data. (mean, median, mode)
median mean = 4mode
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Back to
Instruction
ScaleA scale includes the range of numbers of a
data set, separated by equal intervals.
scale
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SymmetricalIn statistics, data is symmetric if the graph has
a similar shape on either side of the middle.
Back to
Instruction
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Back to
Instruction
Variability
How "spread out" the distribution of data is.
spread out
moreless
spread out
Range
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Standards for Mathematical Practice
MP1: Making sense of problems & persevere in solving them.MP2: Reason abstractly & quantitatively.MP3: Construct viable arguments and critique the reasoning of others. MP4: Model with mathematics.MP5: Use appropriate tools strategically.MP6: Attend to precision.MP7: Look for & make use of structure.MP8: Look for & express regularity in repeated reasoning.
Additional questions are included on the slides using the "Math Practice" Pull-tabs (e.g. a blank one is shown to the right on this slide) with a reference to the standards used.
If questions already exist on a slide, then the specific MPs that the questions address are listed in the Pull-tab.