Exploring Univariate Data · 2018-09-07 · • Press 3 for 3:Add Lists &Spreadsheet to add a new application page. 2. Enter the data for the group in the first column of the spreadsheet

Exploring Univariate Data

T3 PROFESSIONAL DEVELOPMENT SERVICES FROM TEXAS INSTRUMENTS

EXPLORING STATISTICS WITH TI-NSPIRE™ TECHNOLOGY © 2007 TEXAS INSTRUMENTS INCORPORATED

E x p l o r i n g U n i v a r i a t e D a ta Concepts • Mean • Standard Deviation • Dotplots • Boxplots • Median • Quartiles • Interquartile Range • Outliers • Histograms • One Variable Statistics • Standardized Scores • The effect of changing units on

summary measures

Materials • TI-Nspire™ Math and Science

Learning Handheld

Overview This activity describes the steps for investigating univariate data. Students will perform exploratory data analysis using graphical and numerical techniques.

NCTM Standards

Data Analysis and Probability Standard for Grades 9–12

In grades 9–12, all students should have the following knowledge base:

• understand histograms, parallel box plots, and scatter plots; and use them to display data

• compute basic statistics, and understand the distinction between a statistic and a parameter

• for univariate measurement data, be able to display the distribution; describe its shape; and select and calculate summary statistics

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AP Statistics Topics

I. A. Constructing and interpreting graphical

displays of distributions of univariate data, dotplot, stemplot, histogram, and cumulative frequency plot 1. Center and spread 2. Clusters and gaps 3. Outliers and other unusual features 4. Shape

B. Summarizing distributions of univariate data 1. Measuring center: median and mean 2. Measuring spread: range, interquartile

range, and standard deviation 3. Measuring position: quartiles,

percentiles, and standard scores (z-scores)

4. Using boxplots 5. The effect of changing units on summary

measures C. Comparing distributions of univariate

data: dotplots, back-to-back stemplots, and parallel boxplots 1. Comparing distributions of univariate

data: dotplots, back-to-back stemplots, and parallel boxplots

2. Comparing clusters and gaps 3. Comparing outliers

Data Collection

Pose a question: From the time you left home or work until the time you reached your hotel, how long did it take you to travel to this conference? Report your time to the nearest tenth of an hour.

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Getting Started

1. Press c 6 for Home 6:New

Document to open a new TI-Nspire™

handheld document.

• Press 3 for 3:Add Lists &Spreadsheet to

add a new application page.

2. Enter the data for the group in the first

column of the spreadsheet (Figure 1)

3. Arrow to top of the column to the right of

letter A (Figure 2) – can "create" data values.

• Press b 1 2 for Menu 1:Actions,

2:Resize (Figure 3).

• Press ¢ on the NavPad Cursor Controls to

make the column wider.

• Press · d.

• Type in the list name “hours,” and press

· (Figure 4).

4. Save the document with the name Travel.

Figure 1

Figure 2

Figure 3

Figure 4

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Create a New Problem

In order to keep the original data “clean,” a new

problem will inserted, and a copy of the data will

be pasted into the new problem.

1. To select the Lists & Spreadsheet application

page, press / K.

• The border around the page will flash to indicate that the page has been selected.

2. Press / C to copy the page.

3. Press / c (the tools # menu), for

4:Insert, 1:Problem (Figure 5).

4. The list of applications will appear

(Figure 6).

• Do not select an application.

5. Press d, and the words “Press Menu” will

appear (Figure 7).

6. Press / V to paste the spreadsheet.

• The tab (2.1) at the top of the screen indicates that this is problem 2, page 1 (Figure 8).

Figure 5

Figure 6

Figure 7

Figure 8

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Displaying Data using Quick Graph

1. Press ` on the NavPad until the entire

column is highlighted (go up above name).

2. Press b 3 4 for Menu 3:Data,

4:Quick Graph (Figure 9).

• A split screen with a dot plot of the data appears (Figure 10).

Note: The black line at the top of the plot

indicates that the application in the right

screen is currently selected. To move

from the application in the right screen to

the application in the left screen or vice

versa, press / e.

3. The data set and the graph of the data are

linked. Move to the application in the left

screen, and overtype a data value with a new

value within the range of data.

• When you press · to store the new data

value, the plot will change.

• Change two or three data values to observe

this linked relationship.

4. Move to the application in the right screen,

and move the arrow over a data point

(Figure 11).

• Press / a to grab the point.

• The point’s value will appear.

5. Drag the point on the screen until the value

shows two decimal places (Figure 12).

Figure 9

Figure 10

Figure 11

Figure 12

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6. Press a or esc to “drop” the point.

• The point is highlighted, indicating that it is still selected.

• To deselect the point, move the cursor to a clear location on the screen, and press a.

7. Move to the application in the left screen,

and scroll through the list to find the changed

data value (Figure 13) – ctrl tab.

8. In the Lists & Spreadsheet application

screen, highlight the hours column.

• Press b 3 4 for Menu 3:Data,

4:Quick Graph to add another plot.

• The application in the lower right screen is

highlighted and contains a second dotplot

(Figure 14).

9. Press / e until the application in the

upper right screen is highlighted.

• Press b 1 2 for Menu 1:Plot

Type, 2:Box Plot (Figures 15 and 16).

Figure 13

Figure 14

Figure 15

Figure 16

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10. If desired, a third plot may be added using

the Quick Graph command (Figure 17).

Note: What questions would you ask your

students about the travel time? What can

you tell from the graphs about the travel

time that you could not tell by looking at

the data in the spreadsheet?

Exploring Plots and Data

Display Two Plot in a New Window

1. Press c 5 for Home 5:Data &

Statistics to add a new application page

(Figure 18).

• A random display of the data appears.

2. Press / c 5 2 3 for

Tool Menu 5:Page Layout, 2:Select Layout,

3:Layout 3 (Figure 19).

3. A display of the data is shown in the upper

screen. In the application in the lower screen,

the message “Press Menu” appears

(Figure 20).

Figure 17

Figure 18

Figure 19

Figure 20

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4. Press / e to move to the application

in the lower screen.

• Press b 5 for Menu 5:Add Data &

Statistics.

• A second “place holder” plot appears.

5. In the application in the lower screen, move

the cursor to outline the “Click to add

variable” message on the horizontal axis.

• A + sign appears.

• Press a to display the named lists created

in this problem (Figure 21).

6. Press · to select hours.

• A dotplot of the hours data appears. The dotplot is the default univariate plot.

7. Move to the application in the upper screen.

• Following the steps described above, select the hours list on the horizontal axis.

• A dotplot of the hours data appears.

• Change the plot type to boxplot – menu,1,2.

• Click on any dot in the dotplot. What happens?

• Move to any blank space on the screen, and press a to deselect the data.

8. To change the window settings, press

b 4 1 for Menu 4:Window/Zoom,

1:Window Settings (Figure 23).

9. Double the current value of Xmax displayed

in the window settings.

• Press e to outline OK (Figure 24).

• Press ·.

Figure 21

Figure 22

Figure 23

Figure 24

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10. Move to the other graph, and change the

window settings as described above–menu,4,1.

• Both graphs should have the same window settings (Figure 25).

Investigating Data Displayed in a Dotplot and Boxplot

1. Go to the application screen with the boxplot,

and move the cursor along the plot.

• Note the values displayed.

• What information is given in each region of the plot?

• Write the five number summary for this data set.

2. Click on the region between the median and

the third quartile of the boxplot.

• What happens?

• What does this mean in terms of travel time?

3. Move to an open region of the screen.

• An arrow should be displayed.

• Press a to deselect the data.

4. Explore the other regions of the boxplot.

5. Move to the application screen with the

dotplot displayed.

• Suppose that an error was made in recording

one data value. The error could be corrected numerically or graphically.

• Select and drag a point to the right until an outlier appears in the boxplot.

• When did the data value become an outlier?

• What does this mean in the context of this problem?

• Deselect the point – esc.

Figure 25

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6. Pick a point near the center of the dotplot,

and drag it to the right.

• What happens to the boxplot?

• Drag the point to the left.

• What happens to the boxplot?

• What changes in data result in changes in the median or changes in the quartiles?

• What does this mean in the context of this problem?

• Drag the point until the outlier appears again.

• Deselect the point.

7. Select and drag a data point (other than the

outlier) until the outlier is eliminated.

• At what data value did this occur?

• Describe this in terms of the commonly used definition of an outlier.

• Drag the point again to display an outlier.

• Deselect the point.

8. Press b 3 8 for Menu 3:Actions,

8:Plot Value (Figure 26).

9. After the equals sign, type mean, and press

( (open parenthesis).

• Press h · to select the list hours

(Figure 27).

• Press ·, and a vertical line is graphed at

the mean value. Note: The list name may be entered by typing the

name from the keyboard.

Figure 26

Figure 27

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10. Move to the screen with the boxplot

displayed.

• Press b 3 8 for Menu 3:Actions,

8:Plot Value.

• Type MEAN. Press h.Select hours.

• OR - Note that v1 is an option (Figure 28).

• Select v1, the mean of the hours data, and

then press ·.

11. Move to the screen with the dotplot

displayed.

• Select and drag one or more points until the

plotted value for the mean and the median line in the boxplot coincide.

12. Move to the screen with the boxplot

displayed.

• Click on a quartile region. All of the values in that quartile are selected.

• Move to the screen with the dotplot displayed, and drag these selected values.

• Describe what happens to the plots.

Graphing and Exploring a Histogram

1. Press c 5 for Home 5:Data &

Statistics to add a new application page.

2. Move to the “Click to add variable” region

on the horizontal axis.

• Click and select the hours data.

3. Press b 1 3 for Menu 1:Plot

Type, 3:Histogram..

4. Change the window settings, if desired – menu, 4, 1.

Figure 28

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5. Move near the edge of a bin. A hand or the

icon will appear as shown in Figure 29.

• Move closer to the edge of a bin until the

icon shown in Figure 29 appears. Press

/ a.

• Press the left or right arrow key to change the

bin width (menu, 3, 7 will add normal pdf).

• Press a to preserve a particular bin

width.

6. Move to a bar.

• Press a to highlight the bar, and display

its range and frequency (Figure 30).

7. Press / a to grab and move a bar.

• Discuss the results of this action as it relates to the shape of the display.

8. Use the Plot Value tool to graph the mean

and median values of the data set on the

histogram.

9. Discuss the shape of the plot, and relate this

to the location of the mean and the median of

the travel time.

10. The histogram scale options are Count,

Percent, and Density.

• Press b 2 2 for Menu 2:Plot

Properties, 2:Histogram Scale (Figure 31).

• Graph a histogram with a percent scale (2: Percent).

• Then graph a histogram using the density scale (3:Density).

• Observe the y-axis displays for each scale.

Figure 29

Figure 30

Figure 31

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Computing One-Variable Statistics

1. Press / c 2 8 for Tools

Menu 2:Edit, 8:Insert Problem.

2. Press 3 for 3:Add Lists & Spreadsheet.

3. Press / ¡ as many times as necessary to

return to problem one (Page 1.1).

4. Arrow up to highlight column A, and press

/ C to copy the list of data.

• Return to page 3.1, and arrow up to highlight this new list.

• Press / V to paste the data.

5. Press d, and then move to the space to

the right of letter A at the top of the column.

• Enter the list name hours.

• Press ·, and widen the list (menu, 1, 2).

6. Press c 1 for Home 1:Calculator to

add a new application page.

• Press b 6 1 1 for Menu

6: Statistics, 1:Stat Calculations,

1:One-Variable Statistics (Figure 32).

7. Leave 1 as the number of lists, and press

e to outline OK.

• Press ·.

8. Press a to display a drop down menu of

list names.

• Highlight the desired list, and click to choose the list (Figure 33).

• Press e until OK is outlined, and press

· (Figure 34).

Figure 34

Figure 33

Figure 32

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9. Return to page 3.1, and enter the name

minutes in column B.

• Press ·.

10. Click in the formula cell (above cell B1), and

press = – to the left of ctrl.

• Enter 6 0 r, and then

press h.

• Press 3 for 3:Link To:.

• From the drop down menu, choose hours

(Figure 35).

• Press ·.

11. Return to page 3.2, and compute one-variable

statistics for the data in the minutes list (menu, 7:stat, 1: stat calc).

12. Arrow up, and compare the mean and

standard deviation values for the two data

sets.

Standardized Scores

Compute the standardized scores, and compare

the graphs of the raw data and the standardized

scores.

1. Return to page 3.1, and enter the name stdscr

in column C .

• Press ·.

2. Click in the formula cell for column C, and

press =.

• Enter (hours-mean(hours))/stdevsamp (hours).

• Press · (Figure 36).

Figure 35

Figure 36

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Note: Use the VAR, Link To menu to choose

the list name hours. Use the catalogue to

select the standard deviation for the

sample. The word mean may be entered

or selected from the catalogue.

3. Return to page 3.2.

• Press c 5 for Home 5: Data &

Statistics to add a new application page

• Change the layout to top/bottom (Layout 3).

4. In the application in the top screen, graph a

boxplot of the hours data

5. In the bottom screen, press b, and add a

Data & Statistics page.

• Graph a boxplot of the standardized scores (Figure 37).

6. Compare the two plots.

Assessment:

AP Statistics Exam, 2001, Problem 1

AP Statistics Exam, 2002, Form B, Problem 5,

Part (b)

AP Statistics Exam, 2004, Problem 1

Figure 37

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Documents

Exploring Univariate Data · 2018-09-07 · • Press 3 for 3:Add Lists &Spreadsheet to add a new application page. 2. Enter the data for the group in the first column of the spreadsheet