Basic Statistics for a Frequency Distribution

Brief Instructions

Find the class midpoints for your frequency distribution. Press STAT and ENTER. Clear L1 and L2. Enter the class midpoints under L1 and the class frequencies under L2.

TI 83's and Older TI 84's: Press STAT, choose CALC, and press ENTER twice.

Newer TI 84's: Press STAT, choose CALC and press ENTER. You will see a display like the following.

 1-Var Stats List: L1 FreqList: L2 Calculate

Make sure L1 is next to List: and L2 is next to FreqList:, then highlight Calculate and press Enter.

The mean is next to , the sample standard deviation is next to Sx, and the population standard deviation is next to sx.

Detailed Instructions

To demonstrate this procedure, we will use the following frequency distribution:

 Class Frequency 1 - 5 2 6 - 10 3 11 - 15 4 16 - 20 1

First, we must find class midpoints. The class midpoint is the average of the lower class limit and upper class limit for that class. For this example, the class midpoints are

Once you have the class midpoints, you can enter numbers in the calculator. Press the STAT and the ENTER buttons to reach the display with L1, L2, L3 across the top. Under L1 enter the class midpoints, and under L2 enter the class frequencies as shown below. See the Entering Data webpage for instructions on how to do this.

 L1 L2 L3 3 2 8 3 13 4 18 1

TI-83's and older TI 84"s: Press the STAT button, use the right arrow key to choose the CALC option, and press ENTER once. Now you must tell the calculator you are going to be using two lists of numbers in your calculation. So press the following sequence of buttons: 2ND, 1, , (the comma button, just above the 7 button), 2ND, 2. Notice that right above the 1 button is an L1 and right above the 2 button is an L2, so you are telling the calculator to use the lists L1 and L2. Finally, press the ENTER button again.

Newer TI-84's: Press the STAT button, use the right arrow key to choose the CALC option, and press ENTER once. You will see a display like the following.

 1-Var Stats List: L1 FreqList: L2 Calculate

Make sure L1 is next to List: and L2 is next to FreqList:. Press 2nd and 1 to obtain L1 and press 2nd and 2 to obtain L2. Finally, highlight Calculate and press ENTER.

For any of the TI-83 and TI 84 calculators, the statistics are displayed just as when finding basic statistics for a list.

Since the numbers in the original table had no place accuracy, you should use just one decimal place in your estimate for the standard deviation.

As with a list of numbers, the calculator always computes a value for sx even though the table may not contain numbers from each member of the population. Unless the table contains values from the entire population, you should use Sx whenever it is given. Sometimes, when Sx is almost identical to sx, the calculator will only give the value of sx. In these instances, use the sx value as the standard deviation for the frequency distribution.