Skip to content
Class Notes

Lecture Notes for Introductory Statistics, 9th Edition

Lecture Notes for Introductory Statistics, 9th Edition is your perfect study companion, summarizing complex topics from class lectures in an easy-to-follow format.

Preview 16 of 379 pages

See the first 16 pages exactly as they appear in the document.

  1. Page 1
    Read page 1 as text

    Chapter 1 Introduction Use of Technology Statistics is a field that deals with sets of data. After the data is collected , it needs to be organized and interpreted. There is a limit to how much of th e work can be done effectively without the help of some type of technology. The use of technology , such as a calculator with enhanced statistical functions , can take care of most of the details of our work so that we can spend more time focusing on what we are doing and how to interpret the results. Technology can help us not only to store and manipulate data, but also to visualize what the data is trying to tell us. As we work with a calculator, we will be able to:  Enter, revise, and store data.  Perform statistical co m putations on stored data or entered statistics .  Draw graphs (often called plots) based on the data , to help us to understand what useful information can be inferred from that data. Advantages of Using a Calculator There are many good statistical software packages available, such as MINITAB, SAS, and SPSS. Excel also contains many built - in statistical functions , as well as supporting plug ins for statistical work. Still, for the student starting to learn statistics, it’s hard to beat the advantages of using a powerful hand - held calculator.  It is portable and easy to use in many different work environments.  It has battery power that lasts far longer than that of a laptop computer.  It is less expensive than a computer.  It is less expensive than a statistical software package.

  2. Page 2
  3. Page 3
    Read page 3 as text

    2 Advantages to Using the TI - 84 Plus This calculator manual will focus on how to get the most out of using the TI - 84 Plus calculator by Texas Instruments. The TI - 83 was first released in 1996, improving upon its predecessors ( the TI - 81 and TI - 82 ) with the addition of many advanced statistical and financial functions. The TI - 83 Plus and the TI - 84 Plus ha ve essentially the same features as the TI - 83, but with increased memory capacity and a few extra statistical features. The y are powerful calculators with advanced functions, but at the same time easy to use.  Most complicated statistical computations are handled through menus which prompt y ou for the necessary input.  Data entry and revision is handled through a Statistical List Editor that is similar to a s preadsheet in how it is used.  Statistical graphs are handled through menus and important parts of the graph can be r ead by tracing along with the arrow keys.  The calculators are built sturdily and can withst an d many falls off of student desks. Entering and Revising Data This chapter focus es on getting numbers into your calculator and storing them for the organization, interpretation, and analysis part of statistics . When you are not given the necessary statistics to perform calculations, you will need to enter data into the calculator to generate the statistics. We will learn how to do statistical calculations with the calculator in future chapters. Using the Data Editor The data editor in the TI - 84 Plus calculator provides a convenient way to e nter numbers and review them. Numbers from a data set can be stored in a list in the calculator so that we can keep numbers that are related to each other together. Example: Calories Consumed An individual is modifying eating habits and has kept track of calories consumed for the last 10 days, as follows: 1474 , 1633 , 1686 , 1748 , 1326 , 1112 , 1245 , 1539 , 1220 , 1561 If we want to do any sort of analysis o n these numbers, we will need to enter them into the calculator and keep them together as a group.

  4. Page 4
    Read page 4 as text

    3 Accessing the Data Editor Press the  ke y to reveal the STAT menu. To input data or to make changes to an existing set of data values use the data editor , which is number 1 under the EDIT menu . Press  or  key if 1: is highlighted. Resetting the Data Editor If the data editor does not show the columns labeled as L 1 , L 2 , and L 3 , you can re set the e ditor to its default settings by using the SetUpEditor function : Press  . Press  to paste the SetUpEditor function on the home screen . Press  . Once the Editor is set up , return to the Edit function.

  5. Page 5
    Read page 5 as text

    4 Entering Data in the Data Editor T ype in the ten calorie count s under the column labeled L 1 . P ress the  when you are done with one number and ready to move on to the next number. Type in 1 474 and press  . Type in 1633 and press  . Type in 1686 and press  . C ontinue this process until all data values have been entered. Use the up and down arrow keys to move back and forth between the data values . Try changing the value of one of the entries by typing in a new calorie count . Clearing a List of Data Values After a list of data values is no longer needed , you can delete the values by using one of the followi ng methods:  You can highlight each data value and press  . This method is slow and clears the list one data value at a time.  You can highlight the list name, for example L 1 at the top of the column, press  , and then press  .  You can go to the EDIT menu and press  to clear the list as follows: Press  . Press  to paste the ClrList function on the home screen . Press  and then press  to paste L 1 immediately after the ClrList function . Press  . The calculator will display Done to confirm that the list has been cleared.

  6. Page 6
    Read page 6 as text

    5 Entering Lists Directl y to the Statistical Editor List The home screen is where you do most of your calculator work that doesn’t involve menus. From any menu in your calculator , you can always return to the home screen by pressing  and then  (  ) . From the home screen, you can enter data into a list by typing it between a set of braces , { }, and separating the numbers by commas: { 1474 , 1633 , 1686 , 1748 , 1326 , 1112 , 1245 , 1539 , 1220 , 1561 } Once you’ve typed the numbers in to your calculator , you will want to save them for future use . Press  followed by L 1 , L 2 or any other list. (L 1 through L 6 can be accessed by pressing  and then  , or  , or  , etc . ) Note : When you press  key , the screen will display an arrow pointing to the right . Now, press  . Once you’ve store the list as L 1 , you can see the list by typing its name. For example, if you stored the calories in L 1 , typing L 1 (   ) on the home screen will display the list’s contents. (You will need to use  and  to see all of the list’s contents.) Entering Lists Directly to a Name You can also store data to a name d list that you create. From the home screen, type the data values within braces as described above. However, instead of storing the list as L 1 , follow these steps to create a named list: Press  . Press   (  ) to enable the alpha lock. Now, whenever you press a key, the alphabetical letter will display on your screen. Press  ( [C] ). Press  ( [A] ) . Press  ( [L] ). Press  .

  7. Page 7
    Read page 7 as text

    6 Viewing the Named List in the Data Editor The data is stored as the named list CAL , but it cannot be seen in the data editor . To view the data in the data editor : Press  . Press  to enter the data editor . Press  to highlight the name at the top of one of the columns . P ress   (  ) to create a blank column. Type the name of your new list – CAL . Note :  is automatically enabled. Press  . The numbers that you stored in CAL should now appear in the data editor . Create a Named List Within the Data Editor The lists L 1 through L 6 are good places to work with data if you do not need to save the data for later use . If you will need the data later a nd do n o t want to accidentally overwrite it, you can store the data a s a name d list . A list can be named with 1 – 5 characters. The first character must be a letter A - Z or the angle symbol θ ( “theta” ) . The other characters can be a letter, θ , or a number 0 - 9 . To get letters from the keyboard, press  before each letter . The letters appear above and to the right of most of the keys. If you are typing several letters in a row, press   (  ) , type the letters, and then press the ALPHA key again to release the lock. To create a new list named BURN with in the data editor : Press  . Press  to enter the data editor . Press   to highlight the name L 1 at the top of one of the columns . P ress   (  ) to create a blank column between CAL and L 1 . Type the name of your new list – BURN . Note :  is automatically enabled. Press  . BURN should now appear at the top of the column .

  8. Page 8
    Read page 8 as text

    7 The individual also kept track of the number of calories burned by exercising for each of the last 10 days. E nter the following data into the newly named list , BURN . {128, 37, 440, 128, 258, 486, 325, 171, 0, 529} Getting the Names of Lists Some of the calculator commands require that you type in the name of a list. If the name of the list is one of L 1 through L 6 , then you can type it quickly pressing  and the corresponding number key  through  . If the list is a named list , you cannot just type the name of a list from the keyboard using  . List names on the TI - 84 Plus calculator are distinguished from the names of other variables by a small L to the left of the name. Press   (  ) and use the arrow keys to choose one of the list names . T hen press  . Displaying Lists in the Data Edit or You can create custom views in the data editor to display the lists you wish to see. Begin by setting the data editor back to its default setting s : Press   to paste the SetUpEditor function on the home screen. Press  . Press   to enter the data editor. You will see L 1 , L 2 , and L 3 displayed in the data editor. Now suppose you wish to view the CAL and BURN lists at some future time . You must change which lists are displayed in the data editor. Press   to paste the SetUpEditor function on the home screen. Press   (  ) to enter the list menu. Select CAL from the NAMES menu by highlighting it and pressing  . Type  (comma). Select BURN from the NAMES menu by highlighting it and pressing  . Press  . The calculator will display Done , confirming that these lists can now be viewed in the data editor. Press   to enter the data editor. You will see the CAL and BURN lists displayed in the data editor.

  9. Page 9
    Read page 9 as text

    8 Remove a Named List Within the Statistical List Editor In the data , use the arrow keys  ,  ,  , and  to move to the name of the list to be removed. P ress the DEL key for delete . The list disappears, but the contents of the list have not been deleted . To erase the contents of a list , highlight the name of the list and press  and then  . This will leave the list name in the editor and clear its entries. Deleting Lists to Free Up Memory If you store many lists, programs, etc. on your calculator, you may run out of memory. To delete lists from the calculator’s memory: Press   (  ) . S elect 2:Mem Mgmt/Del … Select 4: List … to see all of the current lists. Move the c ursor t o the list that you want to delete and press  .

  10. Page 10
  11. Page 11
    Read page 11 as text

    2 Now that we have told the calculator how to organize the data into classes (bins), we are ready to set up the frequency histogram. Press to view the STAT PLOTS menu. Press . Highlight On and press to turn the plot on. Press to highlight the histogram picture ( ). Press ( ) and select the IPODS list. Leave Freq at 1, since each data value in the IPODS list represents only one point. Now you are ready to draw the frequency histogram. Press to view the histogram. Press to trace the histogram. Press and to move from one bar to the next. You will see the frequency in each class (n = 8) and the range of values in each class (min = 15; max < 20) displayed at the bottom of the screen. The histogram provides us with the following information. C lass Frequency 5 - 9 3 10 - 14 6 15 - 19 8 20 - 24 8 25 - 29 5 Summary of How to Create a Histogram. 1. Enter the data into a list. 2. Determine the range of values for your data, as well as your desired class width. 3. Press and set Xmin , Xmax , Xscl to the range of data values and class width. Set Ymin to 0 and Ymax to a value large enough for the tallest box in the histogram. (You may need to revise this after seeing the histogram.) 4. Press and then to see the STAT PLOT menu. Highlight 4: PlotsOff and press . This will turn off all of the plots.

  12. Page 12
    Read page 12 as text

    3 5. Return to the STAT PLOT menu and select a plot. Turn the plot on by pressing the . Then select the picture of the histogram picture ( ). Enter the name of your data list in Xlist , and leave Freq as 1. 6. Press . Press to display the information needed to create the frequency distribution table. Enter the Frequency Distribution Table into the Data Editor Since the class intervals cannot be entered into a List, the midpoint of each class is used. Such a frequency distribution for the example of the number of Ipods sold would look as follows: C lass Midpoint Frequency 5 - 9 7 3 10 - 14 12 6 15 - 19 17 8 20 - 24 22 8 25 - 29 27 5 Create two new lists, MIDPT and FREQ. Enter the midpoints and frequencies from the table above into two new lists, MIDPT and FREQ, as shown in the screenshot to the right. Create a Frequency Polygon The steps to create a frequency polygon are similar to those needed to create a histogram. Use the data stored in the lists MIDPT and FREQ. Press ( )to get to the STATPLOT menu. Press . Select On . Select the xyline picture ( ). Press ( ) and select the MIDPT list as the Xlist . Press ( ) and select the FREQ list as the Ylist . Select the square as the Mark .

  13. Page 13
    Read page 13 as text

    4 The same WINDOW that was used for the histogram is applicable to the Polygon. Another option is to let the calculator determine the correct window by using the ZOOM menu, as follows: Press . Press the number 9 key to select ZoomStat . Press . Press to trace points in the frequency polygon. Create a Relative Frequency Column A relative frequency column can be generated from the frequency column. Create a new list in the data editor and name it RELFR. With the cursor still highlighting the name RELFR, Press ( ) and select the FREQ list. Press . Press ( ), and press twice to view the MATH menu . Select 5:sum( and press . Press ( ) and select the FREQ list. Press and press . The above sequence of commands calculates each value in the RELFR column by dividing the corresponding value in the FREQ column by the sum of all of the values in the FREQ column. Create a Percentage Column A percentage column can be generated from the relative frequency column. Create a new list named PERC. With the cursor still highlighting the name PERC,

  14. Page 14
    Read page 14 as text

    5 Press ( ) and select RELFR list. Press . Type 100 and press . The above sequence of commands calculates each value in the PERC column by multiplying the corresponding value in the RELFR column by 100. Create a Cumulative Frequency Column A cumulative frequency column can be generated from the frequency column. Create a new list named CUMFR. With the cursor still highlighting the name CUMFR, Press ( ) and press once to view the OPS menu . Select 6:cumSum( and press . Press ( ) and select the FREQ list. Press and press . The above sequence of commands calculates each value in the CUMFR column by adding the corresponding value in the FREQ column to the sum of the previous values in the FREQ column. The table at the right was displayed by using the SetUpEditor to display just these 3 Lists. Create an Ogive For The Cumulative Frequency The steps to create an ogive are very similar to those needed to create a frequency polygon. We will begin by using the data stored under the labels MIDPT, FREQ, and CUMFR. The ogive uses the first lower and all of the upper boundaries rather than the midpoint. Thus it does require an additional data value at the beginning of the list.

  15. Page 15
    Read page 15 as text

    6 Insert a new row of data: Move the cursor to the top value in the MIDPT list (the ‘7’). Press ( ) . A ‘0’ will appear and the rest of the data will shift down. Repeat the above steps for the FREQ and CUMFR columns. Overwrite the values in the MIDPT column with the first lower and all of the upper boundaries, as shown to the left. Press ( )to get to the STATPLOT menu. Press . Select On . Select the xyline picture ( ). Press ( ) and select the MIDPT list as the Xlist . Press ( ) and select the CUMFR list as the Ylist . Select the square as the Mark . Some modifications to the window settings will be needed to incorporate the lower boundary and the increased y-values. Press . Press to trace the points in the ogive.

  16. Page 16
    Read page 16 as text

    1 Chapter 3 Numerical Descriptive Measures After data is collected and organized , the next step is to generate descriptive statistics. Descriptive statistics help you describe the contents of the data set. The two most common measures are measures of ce ntral tendency and measures of dispersion . These measures tell you where the data is centered and how spread out it is , respectively . The center of the data can be described by such statistics as the mean and the median , while the spread of the data can be described by the standard deviation , the range, and the interquartile range . You may also want to describe where one number is with respect to all the other numbers in a large set of numerical data. You can use percentiles to say what percent of the data lies below a given number. After learning about percentiles, another visual display can be created called the box - and - whisker plot. Measures of Central Tendency For Ungrouped Data Example: 20 15 Earnings Before Taxes. Example 3 - 15 gives the 20 15 earnings (in thousands of dollars) before taxes for all six employees of a small company. Enter the 20 15 earnings in to a list named EARN. Calculate The Mean To calculate the mean, or the average, of the 20 15 earnings stored in EARN, go to the home screen - press   (  ) . Press   (  ) and select  . Select 5: sum( and press  . Press   (  ) and choose the list named EARN. Press  ,  ,  , and  . Calculate the Median

363 more pages in the full document

Unlock it once and it stays in your library, ready to chat with or turn into flashcards.

Unlock the full document

More Statistics study materials

See all

Study this document with CramX

Once it is in your library, every tool can work from it.