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www.njctl.org
2015-01-07
6th Grade Math
Data Displays
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Table of Contents
Data DisplaysFrequency Tables and HistogramsBox-and-Whisker Plots
Common Core: 6.SP.4-5(a,b)
Click on a topic to go to that section.
Dot PlotsAnalyzing Data DisplaysGlossary
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Sometimes when you subtract the fractions, you find that you can't because the first numerator is smaller than the second! When this happens, you need to regroup from the whole number.
How many thirds are in 1 whole?
How many fifths are in 1 whole?
How many ninths are in 1 whole?
Vocabulary words are identified with a dotted underline.
The underline is linked to the glossary at the end of the Notebook. It can also be printed for a word wall.
(Click on the dotted underline.)
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Back to
Instruction
FactorA whole number that can divide into another number with no remainder.
15 3 5
3 is a factor of 153 x 5 = 15
3 and 5 are factors of 15
1635 .1R
3 is not a factor of 16
A whole number that multiplies with another number to make a third number.
The charts have 4 parts.
Vocab Word1
Its meaning 2
Examples/ Counterexamples
3Link to return to the instructional page.
4
(As it is used in the
lesson.)
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TablesTicket Sales for School Play
Charts
Graphs
Friday Saturday Sunday
7 PM 78 67 65
9 PM 82 70 30
Matinee NA 35 82
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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.
Next, determine an interval to separate the scale into equal parts.
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
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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
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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: 97 - 39 = 59
SCALE: 59/6 = 9.5555 so 10 would be the size of the intervals
INTERVALS: 30-39, 40-49, 50-59, 60-69, 70-79, 80-89, 90-99
Determine Range, Scale & Interval
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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
95 85 9377 97 7184 63 8739 88 8971 79 8382 85
Create a Frequency Table
Grade Tally Frequency
Click to see answer
Test Grades
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Walking TimeTime Tally Frequency10-19 IIII 420-29 030-39 IIII 540-49 IIII 450-59 060-69 III 3
Pul
lP
ull
Length of Time Walking15 30 15 4545 30 30 6030 60 15 3045 45 60 15
Create a Frequency Table for the data.
Click to see answer
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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
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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
0 30- 40- 50- 60- 70- 80- 90-39 49 59 69 79 89 99
GRADE
Create a Histogram
Note: Frequency tables and histograms show data in intervals
Test Grades
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Que
stio
ns
FREQUENCY
8
6
4
2
0 30- 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?
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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
0 30- 40- 50- 60- 70- 80- 90-39 49 59 69 79 89 99
GRADE
Test Grades
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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
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Create a Frequency Table & Histogram for the following data:
TEST SCORES87 53 9585 89 5986 82 8740 90 7248 68 5764 85
FREQUENCY
8
6
4
2
0 30- 40- 50- 60- 70- 80- 90-39 49 59 69 79 89 99
GRADE
Test Grades
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Compare & Contrast 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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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.
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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
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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
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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.
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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
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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
Note to Teacher
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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
0 30- 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
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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 Grades
Notice that the histogram is more symmetrical. The data is more symmetrically distributed because the scores are closer together.
Mean & Median
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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.
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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.
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A statistical question is a question that creates a variety of answers.
Depending on the question, the data gathered can be numerical (hours spent studying) or categorical (favorite food).
Our focus is on questions that create numerical data.
Statistical Question Non-StatisticalHow many cupcakes of each type were made by the bakery last week?
How many cupcakes were made by the bakery last week?
How many cupcakes did each person in my class eat last week?
How many cupcakes did I eat last week?
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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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Instruction
ConcentratedWhen there is a high frequency of
a value relative to the other values in a set of data.
High
++ +
Concentration
+Low
Concentration
of juice
of juice
100% Concentration
of water
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2
4
6
8
Distribution
The variation and frequency of each value in a set of data.
redbrown
yellowgreenblueorange
773311 Back to
Instruction
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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 8
3,4,6,2, 4,1,8,4,3
# of People in Family
1 2 3 4 5 6 7 8
xxxx
xxxx
x x
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Instruction
Frequency Table
A chart of columns and rows, used to record the values in a data set and how often each value occurs.
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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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IntervalThe equal number of units
between each number on a scale.
0, 5, 10, 15...
Interval of 5 Interval
of 20, 2, 4, 6, 8...
Interval of 100
0, 100, 200...
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Instruction
Measuresof Center
Statistics used to describe the "center" of the distribution of data.
(mean, median, mode)
median mean = 4mode
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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.
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Instruction
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VariabilityHow "spread out" the distribution of data is.
spread out
more
less
spread out
Range
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