Lesson 4: Introduction to Statistics

Lesson 4:
Introduction to Statistics

In this lesson, you will use basic statistic applications and tables to answer the below questions. You will be asked to calculate means, medians, modes and ranges. You will also use conversion factors.

Note: Limited ArcView instructions will be provided in this lesson. Please refer to Lesson 1 for additional ArcView assistance.

If you have not downloaded the data for this lesson, download the data now.

Note to PSD Mac Users:
The Shapefiles (*.shp) and ArcView Project Files (*.apr) for this project are contained in the folder: Mathematics-7th

At this time you may print the Lesson 4 Worksheet to aid you in answering the questions during the lesson.

ArcView Steps for Problem Set 1

Step 1	Open ArcView. Choose Open Project from the File pull-down menu. Navigate to the data directory and open the MathL4.apr. Set your Working Directory.
MAC Users:	Start ArcView by selecting: Macintosh HD \| Documents \| ArcView alias \| Open ArcView and select File \| Open Project \| ArcView Projects \| Mathematics-7th \| MathL4.apr Set your Working Directory.
Step 2	You now want to view the following themes or data layers: fourteeners, continental divide, and counties. To display the themes check the box to the left of the name. With your teacher's permission you may change the colors and symbols displayed in the view window.
Step 3	In order to select and access the data the layer must be active. Make fourteeners the active theme. The button should appear to be raised.
Note:	A fourteener is a mountain peak which has an elevation between 14,000ft and 14,999ft. Colorado has 54 mountains which qualify as fourteeners.
Step 4	Zoom to the extent of fourteeners which is now your active theme.

Questions for Problem Set 1

Note: There are multiple techniques which you can use to begin Question 1. The fourteeners fall close together and therefore it can be difficult for you to count them when you are zoomed out to the full extent. We will explain how to use the select, zoom in, and zoom out tools and how to access the data table to obtain the needed information.

Refer to the statistics section of your textbook for additional math help.

Question 1 First, we want to determine the number of fourteeners on the west side of the Continental Divide.
Which is the west side of the Continental Divide? The left or the right?
Click on the Select button . While holding down the shift key, draw a box around all the fourteeners on the west side of Continental Divide. The selected peaks should be highlighted yellow when selected.
You can toggle back and forth between the Zoom In and Zoom Out button, or you can use the Zoom to extent of active theme button .
Remember, to select the peaks you need to hold down the shift key as you select the peaks.
With the selected peaks highlighted, click on the Table icon . Once the table is open you should see the highlight files. Click on the Promote button . All the highlighted records should be brought to the top of the table. Make sure the Continental Divide column includes only peaks occurring on the west side.
How many fourteeners occur on the west side of the Continental Divide?

Question 2 Continue to use the information highlighted in the table.
What is the mean height, in feet, of the peaks occurring on the west side of the Continental Divide?

Question 3 What is the definition of mean?

Question 4 Convert the answer from Question 2 to meters.
Click here if you need a conversion factor for feet to meters Allmath.com

Question 5 What is the definition of median?

Question 6 What is the median number of the selected elevations?

That's all for Problem Set 1 Click on the Unselect All button . Make sure the table is the active window and select File/Close. With your teacher's permission you may exit Arcview. Click on File/Exit.

ArcView Steps for Problem Set 2

Step 1	If ArcView is already running, open the project called MathL4.apr. Refer to Step 1 of Problem Set 1 for directions on opening the MathL4.apr.
Step 2	Display only the counties theme.
Step 3	Make counties the active theme. The button should appear to be raised.
Step 4	Zoom to the extent of counties which is now your active theme.

Questions for Problem Set 2

Note: Problem Set 2 will use the same ArcView processes as Problem Set 1.

Question 1 For Problem Set 2 we will be determining ranges, means, modes and proportions for Colorado county data.
Select on the following counties: Larimer, Weld, Gunnison, Prowers, Baca, and Elbert. They should be highlighted as you select them. Don't forget to hold down the shift key.
View the corresponding table by clicking on the Table icon.
Next, click on the Promote icon to bring the selected counties to the top of the table.
What information is available for the Colorado county data set?

Question 2 What is the numerical range for the population occurring in the 5 - 17 year old group, for the selected 6 counties?

Question 3 Of the selected counties, which has the highest population and which has the lowest population for the 5 - 17 year old group?

Question 4 What is the mean of the selected counties for the 5 - 17 year old population?

Question 5 What is the definition of a mode?

Question 6 What is the mode for the 30 - 49 year old population in the six selected counties?

Question 7 What proportion of Larimer County in 1997 consisted of the age group 5 - 17 years old? Round to the nearest one-hundredth.

Question 8 Convert the proportion from question 7 to a percent (%).

That's all for Problem Set 2 Click on the Unselect All button . Make sure the table is the active window and select File/Close. With your teacher's permission, you may now exit ArcView. Click on File/Exit.

See data Disclaimer

Go to the HELP page

Go to Lesson 1: Introduction to the ArcView Interface and the Data

Go to Lesson 2: Percentages and Proportions

Go to Lesson 3: Distances and Areas

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Question 1	First, we want to determine the number of fourteeners on the west side of the Continental Divide. Which is the west side of the Continental Divide? The left or the right? Click on the Select button . While holding down the shift key, draw a box around all the fourteeners on the west side of Continental Divide. The selected peaks should be highlighted yellow when selected. You can toggle back and forth between the Zoom In and Zoom Out button, or you can use the Zoom to extent of active theme button . Remember, to select the peaks you need to hold down the shift key as you select the peaks. With the selected peaks highlighted, click on the Table icon . Once the table is open you should see the highlight files. Click on the Promote button . All the highlighted records should be brought to the top of the table. Make sure the Continental Divide column includes only peaks occurring on the west side. How many fourteeners occur on the west side of the Continental Divide?
Question 2	Continue to use the information highlighted in the table. What is the mean height, in feet, of the peaks occurring on the west side of the Continental Divide?
Question 3	What is the definition of mean?
Question 4	Convert the answer from Question 2 to meters. Click here if you need a conversion factor for feet to meters Allmath.com
Question 5	What is the definition of median?
Question 6	What is the median number of the selected elevations?
That's all for Problem Set 1	Click on the Unselect All button . Make sure the table is the active window and select File/Close. With your teacher's permission you may exit Arcview. Click on File/Exit.

Question 1	For Problem Set 2 we will be determining ranges, means, modes and proportions for Colorado county data. Select on the following counties: Larimer, Weld, Gunnison, Prowers, Baca, and Elbert. They should be highlighted as you select them. Don't forget to hold down the shift key. View the corresponding table by clicking on the Table icon. Next, click on the Promote icon to bring the selected counties to the top of the table. What information is available for the Colorado county data set?
Question 2	What is the numerical range for the population occurring in the 5 - 17 year old group, for the selected 6 counties?
Question 3	Of the selected counties, which has the highest population and which has the lowest population for the 5 - 17 year old group?
Question 4	What is the mean of the selected counties for the 5 - 17 year old population?
Question 5	What is the definition of a mode?
Question 6	*What is the mode for the 30 - 49* year old population in the six selected counties?**
Question 7	What proportion of Larimer County in 1997 consisted of the age group 5 - 17 years old? Round to the nearest one-hundredth.
Question 8	Convert the proportion from question 7 to a percent (%).
That's all for Problem Set 2	Click on the Unselect All button . Make sure the table is the active window and select File/Close. With your teacher's permission, you may now exit ArcView. Click on File/Exit.