# Frequency Histograms with a TI-83+ Calculator

The amount of protein (in grams) for a selection of fast-food sandwiches is given below.

23, 30, 20, 27, 44, 26, 35, 20, 29, 29,
25, 15, 18, 27, 19, 22, 12, 26, 34, 15,
27, 35, 26, 43, 35, 14, 24, 12, 23, 31,
40, 35, 38, 57, 22, 42, 24, 21, 27, 33


Suppose we wish to construct a frequency histogram for this data (using a TI-83+ calculator).

First, we go through many of the same steps as those used for constructing a frequency distribution. (Think about it: a histogram is just a graphical representation of the distribution, so it should make sense that we need to start things in a similar way!).

We need to get the values into our calculator, if they aren't already there...

• Hit the STAT button and select EDIT:!ClrList. Now hit the (2nd)L1 button, followed by the ENTER button to clear any previous data in the list L1.
• Now hit the STAT button again, and select EDIT:Edit... followed by the ENTER button. The list editing screen should pop up.
• Use the arrow keys to move the highlighted cell to the first entry of the list L1, if it is not already there.
• Begin typing the values above, hitting the ENTER key after each value to add it to the list.
• When you are done, double check your entries! (You can scroll up and down the list with the arrow keys.) It is VERY easy to make a mistake typing here, and you won't necessarily catch it later -- so look closely now!
• When you are done, hit (2nd)QUIT to return to the home screen.

We need to know our maximum and minimum data values, so...

1. Hit the STAT button, and then select CALC:1-Var Stats followed by the ENTER button. Now scroll down to the bottom of the statistics produced, using the down arrow key. The minimum and maximum data values in list L1 will be named as minX and maxX, respectively.

For the data above, we have a minimum of 12 and a maximum of 57.

We can use these as our minimum and maximum class limits, but round numbers are nice and pretty looking, so you may want to consider lowering your minimum class limit (Just don't stray too far away from the actual minimum!)

In our case, 12 is fairly close to a nice round 10, so let's make that our minimum class limit.

No data values should fall on the borders of our classes. An easy way to stop that from happening is to take your minimum class limit and subtract either .5, .05, .005, or something similar -- so that the number of decimal places of your answer is one greater than the number of decimal places your most precise data has.

For this example, that would make the lowest class boundary 9.5.

There is a slight difference between a "class limit" and a "class boundary".

• A class limit is the smallest or largest data value that would fall into a particular class at a given level of precision (like values with no decimal places, for instance).
• A class boundary doesn't care about the number of decimal places. Anything immediately above it falls into one class, and anything immediately below it falls into another class.

Decide how many classes you want, if this is not already known. You will probably need between 5 and 20 classes, with more classes being more appropriate for larger data sets.

Suppose, for this example, that we want 10 classes.

Now, we need to find out how wide to make each class.

• Subtract your minimum class limit from your maximum, and divide the result by the number of classes you want.

For our example, this calculation yields: (57-10)/10 = 4.7

Now, round this up to the next value with the same precision as your data.

In our example, this would mean rounding 4.7 up to the next integer, which is 5. This is our class width.

We can now start describing our classes.

Our class boundaries start at 9.5 and have width 5, so we have the following classes:

 9.5 - 14.5
14.5 - 19.5
19.5 - 24.5
24.5 - 29.5
29.5 - 34.5
34.5 - 39.5
39.5 - 44.5
44.5 - 49.5
49.5 - 54.5
54.5 - 59.5


To get the calculator to draw the histogram for us:

• Hit the WINDOW button and then
• Set Xmin equal to the left-most class boundary (9.5 in our example)
• Set Xscl equal to our class width (5 in our example).
• Set XMax equal to the right-most class boundary (59.5 in our example, taken from the table above)
• Set Ymin equal to 0. (Since it's impossible to have any classes with less than zero values in them.)
• Set Ymax equal to something a little higher than the largest number of data values that fall into any one class. (You may not know this right away, so as a guess, set it to about n/3, where n is the total number of data values. You can always go back and change this if the histogram is either too tall or too short.)
• Yscl specifies the distance between tick marks on the y-axis, so it should be set to something reasonable for the number of data values in each class. You should be able to use the tick marks to approximate the height of the bar for each class (Set it to 2, for this example)
• Hit the GRAPH button, and you should see something like the following (except it won't be in color).

Now, if you need to draw this histogram somewhere (like on a test or quiz), it would be useful to have some labels on things.

First, label your class boundaries using the list above as a guide.

Now, label the class mark for each class. The class mark is the center value in each class, and can be quickly found by averaging the upper and lower class boundaries for the class in question.

For example, our first class mark is equal to (9.5+14.5)/2 = 12

Finding and labeling these values for each class, we now have

Lastly, label the y-axis appropriately (Remember, we set Yscl equal to 2 earlier, so each tick mark on the y-axis goes up 2 units.)

And we are done!