12  2  4  6 
6  7  8  7 
8  11  8  3 
5  6  7  10 
1  9  7  6 
9  7  5  4 
7  4  6  7 
8  10 

We begin by entering in the data from the in the calculator's list environment. Do this by pressing the button, 

then press the
button to 'edit' (open) the calculator's list environment.
the statement "L1(1)=325" that the red arrow in figure 2 is pointing to is the calculator's way of indicating
that the cursor is in list 1, row 1, and the number in list 1, row 1 is 325. If I press my down arrow key once the cursor moves
down to the second row in L1. Subsequently, the
calculator screens says "L1(2)=325" indicating that the number in list one row two is 325.
Notice I have data in my list 1 that I want to clear out before I enter in the data from the example. 

If you have data in your list that you want to clear out  as I have in list 1 of Figure 2 (above)  then you need to call on the calculator's 'ClrList' command. Press to paste the 'ClrList' command to the calculator's homescreen 

followed by (for L1), then press . The calculator displays a message saying it's 'done.' 

Open the list environment to confirm that your lists are clear by pressing 

If you accidentally delete a list or L1 or another list is not present, like the screen given in figure 6, to get your lists back you have to use the calculator's 'SetUpEditor' command. 

Press to paste the 'SetUpEditor' command to the calculator's homescreen. 

then press The calculator displays a message saying it's 'done.' 

Afterwards, press to edit/open your calculator's list environment,
and check that your lists: L1, L2, L3, etc are displayed.
If your calculator is not displaying L1, L2 and L3 click here for help If your need to clear the contents of list 1 click here for help 

Begin entering in the data from the . Use your arrow keys to make sure your cursor is highlighting the first cell in L1, as shown in Figure 10. 

Then type to enter 12 (the first number in the dataset) into the List One's row 1 (Figure 11). 

Then type to enter the second data value. Then enter the rest of the data values into L1 

Once you get all 30 numbers in L1, use your arrow keys to scroll back through the list and double check that you entered the data in correctly. 

To make the dotplot we need to sort the data set from from least to greatest. We can use the calculator's 'SortA' command. Do this by pressing . 

This will paste the Sort Ascending command to the calculator's homescreen (Figure 15) 

afterwards press (for L1) followed by the button. The calculator displays a message saying it's 'done.' 

Open the list environment by pressing to view the sorted data in list 1. 

We can easily make a frequency distribution table with the sorted data . From figure 18 (left), we can see the first seven numbers of our sorted list. We see that one queen honey bee had 1 mate, another queen honey bee had 2 mates, another had 3 mates and three queen bees had 4 mates. With this information, we can begin constructing our frequency distribution like this: $$ \begin{array}{cc}\hline Number \ of \ Mates & Frequency\\ \hline 1 & 1 \\ 2 & 1 \\ 3 & 1 \\ 4 & 3 \\ \end{array} $$ 

Since there are two fives we add this information to the next row to our table $$ \begin{array}{cc}\hline Number \ of \ Mates & Frequency\\ \hline 1 & 1 \\ 2 & 1 \\ 3 & 1 \\ 4 & 3 \\ \color{red}5 &\color{red} 2\\ \end{array} $$ 

Since there are five sixes we add this information to the next row to our table $$ \begin{array}{cc}\hline Number \ of \ Mates & Frequency\\ \hline 1 & 1 \\ 2 & 1 \\ 3 & 1 \\ 4 & 3 \\ 5 & 2\\ \color{red} 6 & \color{red} 5\\ \end{array} $$ 

Since there are seven sevens we add this information to the next row to our table $$ \begin{array}{cc}\hline Number \ of \ Mates & Frequency\\ \hline 1 & 1 \\ 2 & 1 \\ 3 & 1 \\ 4 & 3 \\ 5 & 2\\ 6 & 5\\ \color{red} 7 & \color{red} 7\\ \end{array} $$ 

Continuing in this fashion gives us this completed frequency distribution for the $$ \begin{array}{cc}\hline Number \ of \ Mates & Frequency\\ \hline 1 & 1 \\ 2 & 1 \\ 3 & 1 \\ 4 & 3 \\ 5 & 2\\ 6 & 5\\ 7 & 7\\ 8 & 4 \\ 9 & 2 \\ 10 & 2 \\ 11 & 1 \\ 12 & 1 \\ \hline total & 30 \ queen \ honey \ bees \end{array} $$ 
To get the Relative Frequency Distribution (Table), we get each relative (percentage) frequency
by dividing each number in the frequency column by 30, the sample size.
$$
\begin{array}{ccc}\hline
Number \ of \ Mates & Frequency& Relative Frequency\\ \hline
1 & 1 & 0.033\\
2 & 1 & 0.033 \\
3 & 1 & 0.033 \\
4 & 3 & 0.010 \\
5 & 2 & 0.067\\
6 & 5 & 0.167\\
7 & 7 & 0.233\\
8 & 4 & 0.133 \\
9 & 2 & 0.067\\
10 & 2 & 0.067 \\
11 & 1 & 0.033\\
12 & 1 & 0.033\\ \hline
total & 30 \ queen \ honey \ bees& 0.999 \\
& & (differs \ from \ 1\\
& & due \ to \ rounding)\\
\end{array}
$$
We could write each relative frequency as a percentage by multiplying each relative by 100. Then the first relative frequency would be 3.3%, and so on. 

We are going to make the calculator plot an ordered pair, (x,y), for each of the 30 sorted data values from the . The xvalue of each point will be the values in L1. To get these points to "stack up," we will enter a yvalue into L2 for each number in L1. In figure 23 (left), we are looking at the first seven (x,y) points. Since the numbers 1, 2 and 3 in L1 don't repeat, the yvalue assigned to each of those numbers is 1. Also notice that in L1, the number 4 occurs 3 times, so the yvalues for those numbers are 1, 2 and 3, respectively. If there had been a fourth 4 in L1 then it's yvalue in L2 would be 4. 

The next 7 sorted data values are listed in list 1 of Figure 19 (left). The 5 in list 1 is the second 5 in the sorted data, so its yvalue in L2 is 2. Notice that the number 6 in L1 occurs 5 times, hence the yvalues in L2 for those five sixes are the natural numbers 1 through 5. 

The next 7 sorted data values are listed in list 1 of Figure 25 (left) along with their yvalues in L2. 

The next 7 sorted data values are listed in list 1 of Figure 26 (left) along with their yvalues in L2. 

The last 6 sorted data values are listed in list 1 of Figure 27 (left) along with their yvalues in L2. 

Before trying to graph the dotplot or any statistics graph on the calculator, it's not a bad idea to change your WINDOW settings to values appropriate for your graph.
The viewing window is the part of the coordinate plane that will be visible on your graphing calculator screen.
Remember that you are only seeing a "portion" of an entire graph in your viewing window.
If you don't know what values are appropriate,
then you could start with the default values.
The default values are Xmin =10, Xmax =10, Ymin =10, and Ymax = 10.

To change the values in the WINDOW
 
Meaning of the numbers in your viewing window
 

To graph the dotplot, or any statistics graph, we need to access the 'STATPLOT' feature of the calculator. Press and you will see a window similar to figure 29 (left) 

Press or to access the settings window for'Plot 1' (figure 30). Right now (figure 30), the plot 1 is turned 'OFF'. Use your arrow keys to move your cursor until it is highlighting the word 'ON' then press 

Use your down arrow to move your cursor to where it is highlighting the first graph 'TYPE' then press . The next thing to do is press your down arrow to get to 'XLIST'. Make sure your 'XLIST' is set to L1, and set your 'YLIST' to L2. Use your down arrows to access your 'XLIST' and 'YLIST' settings. Remember if you need to type L1 then you press and if you need to type L2 then you press 

Now press
What to do if your calculator displayed an error message instead of drawing the graph. 

Now press to access the calculator's ZOOMSTAT command, which tells the WINDOW to adjust its settings by showing the entire statistics Plot 1 (in this case our dotplot) 

Press and change the settings to the ones given in Figure 34 (left) to get a better scaled graph. 

Press to see the result of making the window changes. The graph, using computer software is given below this. 

We can graph a histogram over our dotplot as in the figure directly above from the . Press to access the STATPLOT menu, and press for the PLOT 2 settings window. 

Make sure your Plot 2 is highlighted/selected at the top of the screen (Figure 37). Turn the plot on by using your arrow keys to highlight the word ON then press . Now select the histogram graph type: press your down arrow and then your right arrow twice. The cursor should be highlighting the histogram graph as it is in figure 37 (left). Then press to select the histogram graph type. Arrow down and make sure your Xlist variable is pointing to L1, where the data set is. Set your Freq variable to 1. 

Press
What to do if your calculator displayed an error message instead of drawing the graph. 

You can turn Plot 1 Off by pressing to select the settings window for Plot 1. Then use your arrow keys to move your cursor so that it is highlighting the word OFF, then press 

Afterwards, press to get the histogram by itself. 

Begin the problem by entering the data into your calculator's L1 (list 1).
Figure 41: A dotplot of the data using Roger Palay's dotplot program. (http://courses.wccnet.edu/~palay/math160/tiprogs.htm) 

Press to access your STATPLOT window(figure 42), then press or to open the Plot 1 settings window. (figure 43) 

In order to turn your Plot 1 on, you must use your arrow key to move your cursor to highlight the word ON then press 

The next step is to select the histogram graph type. Press the down arrow, then press the right arrow twice. Afterwards, your cursor should be highlighting the histogram icon. Press to select the hystogram type. Press your down arrow to access your XLIST variable. Make sure your XLIST variable is set to L1. Press for L1. Also make sure your FREQ variable is set to 1 

Then press
(zoom 9 accesses your calculator's ZOOMSTAT command which should zoom in
on the portion of the coordinate plane where the graph is located)
What to do if your calculator displayed an error message instead of drawing the graph. 

When you press the button you can see the values of the window variables were changed by the ZOOMSTAT command. 

If you change your 'Xscl' variable to 1 then press 

you will see a histogram where every number from xmin = 100 to xmax = 138
will have a histogram bar. This is because Xscl = 1 sets the histogram bar width to 1.
This image is identical to the dotplot in figure 41 

If you press the trace key you can see your cursor on top of the first histogram bar corresponding to 100 along the xaxis. The message 'n=1' means that the number 100 degrees occured 1 time in the data set. 

If you press your right arrow repeatedly your cursor will go to the next histogram bar and tell you what the frequency (bar height) of that number is. In figure 50, you can tell that the number 105 degrees occurred 3 times in the data set. Keep pressing the right arrow and in this way you can find the frequency of each number in the sample. We will take this sort of approach when we answer the question posed in the 

To make the frequency table for our we begin writing our table like this: $$ \begin{array}{cc}\hline Record \ Temperatures & Frequency\\ \hline 100 \ to < 105 & \\ 105 \ to < 110 & \\ 110 \ to < 115 & \\ 115 \ to < 120 & \\ \end{array} $$ and so on. To find the correct frequencies for each interval of temperatures in the table, we need to get the correct histogram graph first, and then use our trace key like before. 

Press the button. Make sure that your XMIN variable is set to 100, the first number in the first interval class "100 to < 105". Then set your XSCL variable to 5 and press This should give you the same image as Figure 52 

Press the button. You can see the cursor on top of the first histogram bar which the calculator says corresponds to the first interval class "100 to < 105". Since the figure indicates 'n=2' the frequency of the first class is 2 and our table now looks like this $$ \begin{array}{cc}\hline Record \ Temperatures & Frequency\\ \hline 100 \ to < 105 & \color{red}2 \\ 105 \ to < 110 & \\ 110 \ to < 115 & \\ 115 \ to < 120 & \end{array} $$ 

Press the right arrow button. You can see the cursor on top of the 2nd histogram bar which the calculator says corresponds to the second interval class "105 to < 110". Since the figure indicates 'n=8' the frequency of the 2nd class is 8 and our table now looks like this $$ \begin{array}{cc}\hline Record \ Temperatures & Frequency\\ \hline 100 \ to < 105 & 2 \\ 105 \ to < 110 & \color{red}8 \\ 110 \ to < 115 & \\ 115 \ to < 120 & \\ \end{array} $$ 

Press the right arrow button. You can see the cursor on top of the 3nd histogram bar which the calculator says corresponds to the 3rd interval class "110 to < 115". Since the figure indicates 'n=18' the frequency of the 3rd class is 18 and our table now looks like this $$ \begin{array}{cc}\hline Record \ Temperatures & Frequency\\ \hline 100 \ to < 105 & 2 \\ 105 \ to < 110 & 8 \\ 110 \ to < 115 & \color{red}{18} \\ 115 \ to < 120 & \\ \end{array} $$ 

Press the right arrow button. You can see the cursor on top of the 4th histogram bar which the calculator says corresponds to the 4th interval class "115 to < 120". Since the figure indicates 'n=13' the frequency of the 4th class is 13 and our table now looks like this $$ \begin{array}{cc}\hline Record \ Temperatures & Frequency\\ \hline 100 \ to < 105 & 2 \\ 105 \ to < 110 & 8 \\ 110 \ to < 115 & 18 \\ 115 \ to < 120 & \color{red}{13}\\ \end{array} $$ 

Press the right arrow button. You can see the cursor on top of the 5th histogram bar which the calculator says corresponds to the 5th interval class "120 to < 125". Since the figure indicates 'n=7' the frequency of the 5th class is 7 and our table now looks like this $$ \begin{array}{cc}\hline Record \ Temperatures & Frequency\\ \hline 100 \ to < 105 & 2 \\ 105 \ to < 110 & 8 \\ 110 \ to < 115 & 18 \\ 115 \ to < 120 & 13\\ 120 \ to < 125 & \color{red}{7}\\ \end{array} $$ 

Press the right arrow button. You can see the cursor on top of the 6th histogram bar which the calculator says corresponds to the 6th interval class "125 to < 130". Since the figure indicates 'n=1' the frequency of the 6th class is 1 and our table now looks like this $$ \begin{array}{cc}\hline Record \ Temperatures & Frequency\\ \hline 100 \ to < 105 & 2 \\ 105 \ to < 110 & 8 \\ 110 \ to < 115 & 18 \\ 115 \ to < 120 & 13\\ 120 \ to < 125 & {7}\\ 125 \ to < 130 & \color{red}{1}\\ \end{array} $$ 

Press the right arrow button. You can see the cursor on top of the 7th histogram bar which the calculator says
corresponds to the 7th interval class
"130 to < 135". Since the figure indicates 'n=1' the frequency of the 7th class is 1 and our table now looks like this
$$ \begin{array}{cc}\hline
Record \ Temperatures & Frequency\\ \hline
100 \ to < 105 & 2 \\
105 \ to < 110 & 8 \\
110 \ to < 115 & 18 \\
115 \ to < 120 & 13\\
120 \ to < 125 & {7}\\
125 \ to < 130 & 1\\
130 \ to < 135 & \color{red}{1}\\ \hline
Total & 50 \ temperatures
\end{array}
$$
There are no more histogram bars, for if there were, we would have seen them when we pressed [ZOOM][9] (for ZOOMSTAT). Another indication
that there are no more histogram bars is the fact that all the frequency numbers in the table add up to 50, the same number of measurements in the
data set. Therefore the completed Frequency Distribution is listed above.
If we wanted to get a relative frequency distribution, then we simply need to add on a third column to our table and list each relative frequency. Each relative frequency is found by dividing the frequency of each class by 50, the sample size. 
The relative frequency distribution looks like this: $$ \begin{array}{ccc}\hline Record \ Temperatures & Frequency& Relative Frequency\\ \hline 100 \ to < 105 & 2 & 0.04 \\ 105 \ to < 110 & 8 & 0.16 \\ 110 \ to < 115 & 18 & 0.36 \\ 115 \ to < 120 & 13 & 0.26 \\ 120 \ to < 125 & {7} & 0.14 \\ 125 \ to < 130 & 1 & 0.02 \\ 130 \ to < 135 & {1} & 0.04 \\\hline Total & 50 \ temperatures & 1 (100\%) \end{array} $$ We can write relative frequencies as decimals or percents. For example, the first relative frequency is 4%, the second is 16%, the third is 36%, and so on. 