Technology: Summary Statistics on the TI-84

So far we've created graphs and summary statistics "by hand' but that can quickly become cumbersome, so we often rely on technology to perform these tasks more quickly. The instructions below will guide you through working on the TI-83 or TI-84 to compute summary statistics for a single quantitative variable and graph histograms and boxplots.

Property taxes
Let's work with the following data about the single-family residences on a street in Edmonds, Washington. I collected this data on October 3, 2006, from the Web site of the Snohomish County Assessor. For each house I recorded the house number, the size (in square feet), the 2007 assessed value (in thousands of dollars), the lot size (in acres), the 2006 taxes (in dollars) and the number of stories. Here is the complete data set:

house	size	assess	lot	taxes	stories
20911	1561	304	0.2	2604	1
20912	1038	297.6	0.2	280	1
20918	1224	289.5	0.17	2353	1
20921	1232	292.8	0.17	756	1
20924	1995	314.6	0.17	2620	2
20927	1714	322.7	0.18	2632	1
20930	1832	336.1	0.18	2779	2
21003	1095	279	0.18	2321	1
21006	2011	319.5	0.18	2663	2
21015	1366	289.3	0.18	2415	1
21018	1292	301.4	0.18	2477	1
21023	1458	314.3	0.18	1386	1
21028	2031	320.9	0.18	2676	2
21105	1366	304	0.18	2473	1

Let's graph one of the quantitative variables. We'll start with the 2007 assessed value.

First, turn the calculator on by pressing the ON key at the lower-left corner. Before we can graph data using the calculator, we need to enter the data into a list. The TI-83 and TI-84 have six built-in lists, called L1, L2, L3, L4, L5 and L6. To access the lists, press STAT:

(To complicate matters there is also a LIST menu above the STAT key, but we don't want to use this right now, so ignore it for the time being.)

Next press ENTER and you should be in the list editor:

Use the arrow keys to move up and down in a list, or the left and right arrows to move from one list to another.

If a list you want to use already contains data and you want to clear the list, move the cursor up so that the list name (e.g. L1) is highlighted:

then press CLEAR and ENTER; all of the data in the list should disappear. DO NOT press the DEL key when the list name is highlighted: this will delete the entire list, rather than its contents. To restore a deleted list move the cursor to the name of another list, press 2ND and then INS (for insert, above the DEL key), then press 2ND and then L1 (above the 1 key, or another key for the name of the list you want to insert). You can, however, use the DEL key to delete a single entry in a list.

To enter data once the entries in the list have been cleared, move the cursor to the first position in the list, type a number, then press ENTER. Repeat this until you have entered all of the data. If you enter the 2007 assessed value data into list L1 on your TI-84 (from here on out I'll just write "TI-84" so that I don't have to type "TI-83 or TI-84" repeatedly) your screen should look something like this:

Notice that when you move the cursor over the last entry in the list it says L1(14) = 304. This means that the 14th entry in list L1 is 304. Because there are 14 houses in the data set, this is what we want to see.

To exit the list editor, press 2ND then QUIT (above the MODE key).

We can now draw a histogram with the TI-84 using the assessed value data in list L1. Press 2ND then STAT PLOT (above the Y= key) to get to the STAT PLOTS menu:

then press ENTER to select Plot1:

Move the cursor over On and press ENTER to turn on Plot1:

Now move the cursor down and then right two spaces so that it highlights the histogram icon, then press ENTER:

If Xlist is not already set to L1 (or the name of the list with your data), move the cursor down, then type L1 (2ND and then the 1 key) and press ENTER to designate L1 as the Xlist.

If Freq is not automatically set to 1 (it usually is) then you'll need to reset it to 1. For some reason, the TI-84 defaults to the alpha-lock when this entry is highlighted; if you need to change the frequency to 1 from something else, you'll need to press ALPHA to turn off the alpha-lock, then type the number 1. Your screen should then look something like what you see above.

Now press ZOOM, then move the cursor down to ZoomStat:

and press ENTER. This is usually the most expedient way to choose an appropriate window, but you may still need to adjust the window slightly. Here is the histogram you should get using ZoomStat:

To manually adjust the window settings, press the WINDOW button, then enter suitable values and press GRAPH. You can experiment with different WINDOW values, which may give you different histograms. If you change the WINDOW values as follows:

and press GRAPH you should get a histogram that looks like this:

Be aware that we sometimes get vastly different histograms simply by adjusting the starting point and the bar width. We might say that the above histogram appears bimodal, while the original histogram appeared to have an outlier that is not visible in our second histogram.

Note that there is no scale indicated in this histogram, nor is the horizontal axis labeled with a variable name or units. Whenever we draw a histogram we should include all of these labels if technology permits.

On occasion, quantitative data is displayed in a frequency table, much like those we created for categorical variables. This usually occurs when the quantitative variable only takes on discrete values, or is conveniently rounded to an integer.

For example, in Fall 2006 students in my online statistics class were given an unlimited number of attempts to take a 5-point quiz. We could display the number of attempts like this:

attempts	count
0	3
1	8
2	8
3	4
4	2
5	2
6	1

If we wanted to enter this data into the TI-84 to create a histogram, we could enter 0 three times, then 1 eight times, then 2 eight times, and so on into a list until the list had 28 entries, one for each student. But there's another way. We can enter the number of attempts (the left column) into one list (say L1) and the counts into the next list (say L2):

We then follow the same steps as before, except we type L2 for Freq in the STAT PLOT menu:

To get a histogram we can use ZoomStat:

Compare this with the stem-and-leaf display we created previously:

0|6
0|55
0|44
0|3333
0|22222222
0|11111111
0|000

0|6 = 6 attempts

Summary statistics
Now let's compute the summary statistics for the 2007 assessed value variable in the house data set.

Enter the assessed value data into a list, say L1, then press 2ND and QUIT (above the MODE key), as you did to create a histogram. Now press STAT, move the cursor to the right to highlight CALC and notice that 1-Var Stats is already highlighted:

Press ENTER and type L1 (2ND and then the 1 key). Your screen should look like this:

Now press ENTER. The calculator will display many different values:

These values are:

• `bar x` (the mean)
•  `sum x` (the sum of the values in L1; you can ignore this for now)
• ` sum x^2` (the sum of the squares of the values in L1; you can ignore this as well)
• Sx (the standard deviation of the values in L1; we simply call it s)
• `sigma x` (the population standard deviation; we will NEVER use the TI-84 to calculate this, so always ignore this part of the 1-Var Stats output)
• n (the number of data values in L1)

So far we can see that the mean of the 2007 assessed property values for homes in my neighborhood is $306,121, with a standard deviation of $15,898. You could compute these statistics "by hand" but it would take a ridiculously long time: ALWAYS use the calculator or computer to compute summary statistics, especially the standard deviation.

But there's more! Use the down cursor to scroll down the screen as far as you can. You should see:

We can now read off the 5-number summary:

• minX (the minimum data value in L1)
• Q1 (the first quartile of the values in L1)
• med (the median of the values in L1)
• Q3 (the third quartile of the values in L1)
• maxX (the maximum of the values in L1)

Boxplots
To draw a boxplot of the assessed value data, follow the instructions above for making a histogram, but choose the boxplot (or modified boxplot to show outliers) icon instead of the histogram icon:

Then use ZoomStat to get the boxplot:

We can see a bit more clearly from the boxplot that the data is skewed positively (but notice that we can't tell if the data set is unimodal or bimodal from the boxplot, so we should look at both a histogram and a boxplot whenever possible). Note again that the axis isn't labeled and no scale is indicated, so this would not be a satisfactory graph on a HW solution, exam or project.

Summary statistics from frequency tables
Returning to the data about the number of attempts students in my Fall 2006 online class made on a 5-point quiz, we can, as before, enter the number of attempts (the left column) into one list (L1) and the counts into the next list (L2). Now type 1-Var Stats L1 as above, but then type , (a comma, above the 7 key) and then L2:

Now press ENTER to get the summary statistics for the quiz attempts by the 28 students: