Measures of Central Tendency

1. The first way we will consider is the following: If all the bolts had equal length and the sum of all the bolts' lengths was the same as it is in the sample, how long would each bolt be? You are probably familiar with this way of describing data already. How would you describe the height of the students in your class? You would probably calculate the mean (average) height by calculating the sum of the heights of all the individual students, and then divide by the total number of students. That is the same as saying how tall each person would be if all persons were the same height, and the sum of heights of these students was the same as it is now in your class.

2. The second possibility is to ask: Which length occurs most frequently? You can answer that question by looking at the frequency table you created. The highest frequency in the table is found next to the lenght that occurs most often. That length is called the mode. This is often the best way to describe a set of data. If, for example, you want to describe the color of all the cars in Indiana, you could hardly calcualte the average color, the only way is to say which color is found on most cars, which color is the most popular one. What do you think is the mode for the color of cars in Indiana?

3. The third possibility is to find a number such that half of your sample is below that number, and the other half is above the number. In the case of Screws and Bolts Inc. you would find an imaginary bolt, such that half of the bolts in the sample is shorter than that bolt, and half of the bolts in the sample is longer than it. The length of the imaginary bolt is called the median.

You can, of course, use your TI calculator to calculate the mean and the median. In fact, most scientific calculators can at least find the mean for you. 

When you created the histogram in the previous activity, you entered the data for Screws and Bolts Inc. into lists L1 and L2 on your calculator. Now, you can let the calculator find the mean and the median based on the data you already have entered. 

Begin by pressing the STAT key. Select EDIT, just to make sure your data are still there.  If not, return to the previous activity where you will find directions on how to enter data.
When the data are in their place in lists L1 and L2, press the STAT key and choose SetUp by pressing 3.
On the SetUp screen you can move around by using the arrow keys.  We will only be concerned with 1-Var Stats for now.  Use the arrows to move to L1 in the Xlist line.  Press ENTER.  Then move to L2 in the Freq line and press ENTER.
Press the STAT key, select CALC by pressing the right arrow key.  Then press 1 to select 1-Var Stats.  Press ENTER.
The mean and the median are in the list of numbers you can see on the calculator screen. The mean is the first number you see (x with a bar over it), and the median is labeled Med.
Which one of the two numbers do you think is a better description of the data?  Before you answer the question you may want to take another look at your histogram.