6th Grade - NJCTLcontent.njctl.org/courses/math/6th-grade-math/data... · 6th Grade Data Displays 2015-12-01 Slide 2 / 85 Table of Contents ... 4 2 0 30- 40- 50- 60- 70- 80- 90-39

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6th Grade

Data Displays

2015-12-01

www.njctl.org

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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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http://www.njctl.org

http://www.njctl.org

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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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Teac

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in the presentation. The text box the word is in is then linked to the page at the end of the presentation with the word defined on it.

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Data Displays

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Contents

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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

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Frequency Tables & Histograms

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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

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


This question address MP6 - Attend to precision.

Ask:

- Why is it important to be precise when determining the intervals?

- What common student errors can occur when calculating these values?

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


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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95 85 9377 97 7184 63 8739 88 8971 79 8382 85

Grade Tally Frequency

Test Grades



Ans

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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


Length of Time Walking 15 30 15 45 45 30 30 60 30 60 15 30 45 45 60 15


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Length of Time Walking 15 30 15 45 45 30 30 60 30 60 15 30 45 45 60 15



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Walking TimeTime Tally Frequency10-19 IIII 420-29 030-39 IIII 540-49 IIII 450-59 060-69 III 3

Range: 60 - 15 = 45Interval: 45/5 = 9 so 10


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

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GRADE

Test Grades

Histogram

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Test Grades

95 85 9377 97 7184 63 8739 88 8971 79 8382 85

FREQUENCY

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GRADE

Test Grades

Note: Frequency tables and histograms show data in intervals

Create a Histogram

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FREQUENCY

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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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FREQUENCY

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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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MP8 - Look for and express regularity in repeated reasoning

Ask:

- How are histograms and bar graphs alike?

- How are histograms and bar graphs different?

- Why are there no spaces between the bars of histograms?


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.

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GRADE

Test Grades

Histogram

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TEST SCORES95 85 9377 97 7184 63 8739 88 8971 79 8382 85

EXAMPLE:

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FREQUENCY

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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

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GRADE

Test Grades

Histogram Practice

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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

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GRADE

Test Grades

Histogram Practice

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MP1 - Make sense of problems and persevere in solving them.

Ask:

· What information would you start with?

· Which would you start with, the Histogram or the Frequency

Table, and why?

· What steps will you take to make the table and histogram?

FREQUENCY

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040- 50- 60- 70- 80- 90-49 59 69 79 89 99

GRADE

Grade Tally Frequency40-49 II 250-59 III 360-69 II 270-79 I 180-89 IIII II 790-99 II 2


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

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GRADE

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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

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GRADE


Mat

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Ask:

- What are the benefits of using a bar graph vs. a histogram? Vice versa?

- What about the given information would make one choice better than the other?


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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Box and Whisker Plots

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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


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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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1 The minimum is

A 87B 104C 122D 134

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1 The minimum is

A 87B 104C 122D 134


Ans

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A


2 The median is

A 87B 104C 122

D 134

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2 The median is

A 87B 104C 122

D 134


Ans

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C


3 The lower quartile is

A 87B 104C 122D 134

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3 The lower quartile is

A 87B 104C 122D 134


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B


4 The upper quartile is

A 87B 104C 122D 134

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4 The upper quartile is

A 87B 104C 122D 134


Ans

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D


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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A the minimum and medianB the minimum and maximumC the lower quartile and maximum

D the minimum and the upper quartile


Ans

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C & D



A the minimum and medianB the minimum and maximumC the lower quartile and upper quartileD the median and maximum

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Ans

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A, C & D




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Ans

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B


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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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



Ans

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Minimum 88Lower Quartile 105Median 22Upper Quartile 133Maximum 148


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

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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



Ans

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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


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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8

True



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


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


Ans

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False


9

True



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


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



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


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


Ans

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False


10

True



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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10

True



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


Ans

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False


11

True



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.

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False

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11

True



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


Ans

wer

False


12

True



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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12

True



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


Ans

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True


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

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



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Minimum = 26Lower Quartile = 38Median = 43.5Upper Quartile = 56Maximum = 73


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


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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



Ans

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Minimum = 107Lower Quartile = 133Median = 144.5Upper Quartile = 153.5Maximum = 155


Return toTable of

Contents

Dot Plots

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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:

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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?

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xxxxxx

xxx

xxx

xxxx

xx

xxx

xxxxx

Test Scores

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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26 studentsMinimum = 30Maximum = 50Mean # 40.1Mode = 30Median = 40Lower Quartile = 35Upper Quartile = 48

MP 7 - Look for and make use of structure.

Ask -

- Where have we seen mean, median, and mode before?

- How can we use how we make a histogram and bar graph to now make a dot plot?


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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1 2 3 4 5 6 7 8 9 10



How many miles is Miley most likely to bike on her last day?


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1 2 3 4 5 6 7 8 9 10



How many miles is Miley most likely to bike on her last day?



Ans

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Use dual-screen mode to mark the x's on the number line.

1 2 3 4 5 6 7 8 9 10

x

xxxx

xxx

xxxxx

xx

xxxx x


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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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

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xxx

xxxx

Test Scores

Dot Plot Practice


Teac

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Use dual-screen mode and pin this screen to show the dot plot during responder questions.


13 What does each data item or "x" represent?

A the teacherB a studentC the test scoreD the entire class

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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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B


14 How many more students scored 75 than scored 85?

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14 How many more students scored 75 than scored 85?


Ans

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1


15 What is the median score?

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15 What is the median score?


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85


16 What is the lower quartile of the test scores?

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16 What is the lower quartile of the test scores?


Ans

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80


17 The upper quartile is 90.

True

False

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17 The upper quartile is 90.

True

False


Ans

wer False

The upper quartile is 92.5


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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18 What percent of the students scored an 80 or above on the test?

A 25%B 50%C 75%D 100%


Ans

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C


19 What is the interquartile range of the test scores?

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19 What is the interquartile range of the test scores?


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12.5


20 What is the mean of the test scores?

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20 What is the mean of the test scores?


Ans

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86.2


21 What are the mode(s) of the data set?

A 75B 80C 85D 90E 95F 100

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21 What are the mode(s) of the data set?

A 75B 80C 85D 90E 95F 100


Ans

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A & D


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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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



Ans

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5


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


E greater

F less

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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


E greater

F less[This object is a pull tab]

Ans

wer C 5/8

E greater





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

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Analyzing Data Displays

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Contents

Slide 60 / 85

A data display shows us a lot of information about the measures of center

Find the:

Mean _____Median _____Mode _____Range _____


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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A data display shows us a lot of information about the measures of center

Find the:



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[This object is a pull tab]

Ans

wer Mean 77

Median 83Mode 70 and 83Range 53


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.

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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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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.

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GRADE

Test Grades

Notice that the histogram is not symmetrical. The data is pulled to the left because some students scored low.

MedianMean



MP3 - Construct viable arguments and critique the reasoning of others.

Have students discuss with each other: - What is causing the distance between the mean and the median?- If the mode is not the best choice to describe the data set, what would be a better choice?- What can tell us how well most of the students performed on the test?


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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

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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


Slide 63 / 85

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

Slide 64 / 85

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

Slide 65 / 85

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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:


Analyzing Dot Plots

Slide 66 / 85

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:


Analyzing Dot Plots


Ans

wer Mean 3.9

Median 3Mode 3Range 9


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

Slide 67 / 85

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


Ans

wer

The dot plot is not symmetrically distributed. Although much of the data is concentrated around the median it is pulled to the right because of the few students who volunteered many hours.Therefore, the mean is greater than the median.


24 The median is greater than the mean. Explain your answer. (Determine by analyzing the graph instead of using a calculator.)

True

False

Slide 68 / 85

24 The median is greater than the mean. Explain your answer. (Determine by analyzing the graph instead of using a calculator.)

True

False


Ans

wer False

The data is distributed towards the right and the median is 3.


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

Slide 69 / 85

25 Which measure of center appropriately represents the data?

A MeanB Median


Distance (ft)

FREQUENCY

4

3

2

1

0 0-4 5-9 10-14 15-19 20-24

C Mode


Ans

wer

B or C

The data is pulled towards the left making the median a more appropriate choice. There is only one mode and it is centered in the data making it a good representation of the data.


26 The number that is represented by the smallest interval on this histogram is called the ______________.


Distance (ft)

FREQUENCY

4

3

2

1

0 0-4 5-9 10-14 15-19 20-24

Slide 70 / 85

26 The number that is represented by the smallest interval on this histogram is called the ______________.


Distance (ft)

FREQUENCY

4

3

2

1

0 0-4 5-9 10-14 15-19 20-24


Ans

wer

Outlier


27 The students in the older half of the group are

A very close in ageB not so close in ageC cannot be determined

Slide 71 / 85

27 The students in the older half of the group are

A very close in ageB not so close in ageC cannot be determined


Ans

wer

BThis is because the upper

quartile is closer to the median so their ages vary more than the

younger group.


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

Slide 72 / 85

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


Ans

wer A

The students in this interval are the closest in age to each other

because the interval is small.


Glossary & Standards

Return toTable of

Contents

Slide 73 / 85

page16svg

Glossary & Standards

Return toTable of

Contents


Teac

her N

otes Vocabulary Words are bolded

in the presentation. The text box the word is in is then linked to the page at the end of the presentation with the word defined on it.


Back to

Instruction


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

+

Slide 74 / 85

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

Slide 75 / 85

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page0svg

page70svg

2

4

6

8

DistributionThe variation and frequency of

each value in a set of data.

redbrown

yellowgreenblueorange

773311

Back to

Instruction

Slide 76 / 85

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

Slide 77 / 85

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.

Slide 78 / 85

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page46svg

page20svg

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

Slide 79 / 85

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...

Slide 80 / 85

Back to

Instruction

Measures of CenterStatistics used to describe the "center" of the

distribution of data. (mean, median, mode)

median mean = 4mode

Slide 81 / 85

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Back to

Instruction

ScaleA scale includes the range of numbers of a

data set, separated by equal intervals.

scale

Slide 82 / 85

SymmetricalIn statistics, data is symmetric if the graph has

a similar shape on either side of the middle.

Back to

Instruction

Slide 83 / 85

Back to

Instruction

Variability

How "spread out" the distribution of data is.

spread out

moreless

spread out

Range

Slide 84 / 85

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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.

Slide 85 / 85

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.


Mat

h Pr

actic

e


Documents

6th Grade - NJCTLcontent.njctl.org/courses/math/6th-grade-math/data... · 6th Grade Data Displays 2015-12-01 Slide 2 / 85 Table of Contents ... 4 2 0 30- 40- 50- 60- 70- 80- 90-39