SAT Test Prep #1: Mean, Mode, and Median on the TI-83 Plus, TI-84 Plus, and TI-89

Filed under Difficulty: Easy, SAT, Statistics, Test Prep, TI-83 Plus, TI-84 Plus, TI-89.

The following is a sample SAT problem similar to many found on the actual exam:

Nighttime Temperatures in Juneau, Alaska

Mon Tue Wed Thu Fri Sat Sun
32 28 28 26 21 22 25

The table above shows the temperatures, in degrees Fahrenheit, in a city in Alaska over a one-week period. If m represents the median temperature, f represents the temperature that occurs most often, and a represents the average (arithmetic mean) of the seven temperatures, which of the following is the correct order of m, f, and a?

(A) a < m < f
(B) a < f < m
(C) a = m < f
(D) m < f < a
(E) m < a < f

This tutorial shows how to solve this problem and then how to use your TI-83 Plus, TI-84 Plus, or TI-89 to simplify the process.

Mean, Median and Mode: Mathematical Solution

In order to solve this problem, we have to perform three calculations to find the mean, median and mode of the nighttime temperatures (the data set), then choose the correct ranking of the mean, median and mode from the multiple choices that are provided.

To find the arithmetic mean (also called the average) of a set of data, add up each data point and divide by the total number of data points, in this case 7. The mean for this problem is (32 + 28 + 28 + 26 + 21 + 22 + 25)/7 = 182/7 = 26.

To find the median of a set of data, order the numbers from smallest to largest and choose the data point in the middle. If you have an even number of data points, then average the middle two numbers in the list. In the example above we have an odd number of data points, so we can just choose the middle numbers after re-ordering them. Ordering the temperatures in the problem we get: 21 22 25 26 28 28 32. The median is 26.


The data point in a set which occurs the most often is also known as the mode, and can be more than one number if multiple numbers appear the greatest number of times. For example, the list {22, 22, 24, 26, 26} has modes of 22 and 26. The only data point that appears more than once in our table is 28, so the mode of the data is 28.

We know that a=26, m=26, and f=28, so the correct answer is (C).

Solution with TI-83 Plus or TI-84 Plus

Fortunately, we can enter the data provided in this SAT problem into our calculator to save time. It takes a little effort to key the data into your calculator, but you only have to enter it once.

From the home screen, press STAT 5 ENTER. This sets up the default list editor. Then press STAT ENTER to select the list editor. We’re going to use L1 for this tutorial–if it has data in it, select the name with the arrow buttons and press CLEAR ENTER to empty it. Now enter the list of temperatures into L1 by using the arrow buttons to select a cell, then pressing ENTER, typing in the corresponding number, and pressing ENTER again to confirm.

sat1 mode 83 000 SAT Test Prep #1: Mean, Mode, and Median on the TI 83 Plus, TI 84 Plus, and TI 89

Next press 2nd STAT to select the list math menu. Press 3 to paste the mean( function to the home screen.

sat1 mode 83 001 SAT Test Prep #1: Mean, Mode, and Median on the TI 83 Plus, TI 84 Plus, and TI 89

Press 2nd 1 to type L1, and press ENTER to evaluate. This returns the mean of the entered list.

sat1 mode 83 002 SAT Test Prep #1: Mean, Mode, and Median on the TI 83 Plus, TI 84 Plus, and TI 89

Navaigate again to the list math menu by pressing 2nd STAT . Press 4 to paste the median( function to the home screen. Press 2nd 1 to type L1, and press ENTER to evaluate. This returns the median of the entered list. Note that for this set of data, the median the mean are the same.

sat1 mode 83 003 SAT Test Prep #1: Mean, Mode, and Median on the TI 83 Plus, TI 84 Plus, and TI 89

Another way to look at these statistics is by pressing STAT ENTER to paste 1-Var Stats to the home screen. Press 2nd 1 to specify L1 and then press ENTER to enter the one-variable statistics screen.

sat1 mode 83 004 SAT Test Prep #1: Mean, Mode, and Median on the TI 83 Plus, TI 84 Plus, and TI 89

This screen displays the mean as x-bar and the median under Med, as well as a host of other statistics.

sat1 mode 83 005 SAT Test Prep #1: Mean, Mode, and Median on the TI 83 Plus, TI 84 Plus, and TI 89

Unfortunately, there isn’t a built-in function to calculate the mode of a list on the TI-83 Plus and TI-84 Plus. Fortunately, Calcblog provides a program to do this which you can download here.

To use our program, press PRGM, select MODE, press ENTER to paste it to the home screen, and ENTER again to run.

sat1 mode 83 006 SAT Test Prep #1: Mean, Mode, and Median on the TI 83 Plus, TI 84 Plus, and TI 89

Then press 2nd 1 ENTER to specify L1 as the data you want to find the mode of. Alternately, you can enter the data as a list in the program. To do this, press 2nd ( to enter a bracket, and then enter your data separated by commas and press ENTER when done.

sat1 mode 83 007 SAT Test Prep #1: Mean, Mode, and Median on the TI 83 Plus, TI 84 Plus, and TI 89


Solution With TI-89

First, your calculator must have the necessary software. If you have a TI-89 Titanium or other newer calculator, then you should have a Stats/List Editor icon on your Apps screen. Otherwise, you should have a Stats/List Editor application in your Flash Apps folder. (Reached by pressing APPS then ENTER). If you don’t have this software or you aren’t sure, you can download it here.

screenshot000 SAT Test Prep #1: Mean, Mode, and Median on the TI 83 Plus, TI 84 Plus, and TI 89

Next, start the Stats/List Editor application. For most calculators this can be reached by pressing APPS then ENTER to get to the Flash Apps menu, then finding the application and pressing ENTER, though if your calculator has an APPS menu with icons, you don’t need to find a separate “Flash Apps” menu.

At this point, if you’re asked which folder you want to be in, just press ENTER to select the default (main). You will then be taken to the list editor, which is similar to that on the TI-83+/TI-84+ series of calculators.

screenshot001 SAT Test Prep #1: Mean, Mode, and Median on the TI 83 Plus, TI 84 Plus, and TI 89

We’re going to be using list1 for this tutorial–if it has data in it, clear the list by selecting the name with the arrow buttons and pressing CLEAR, then ENTER. Enter the temperatures by using the arrow buttons to select a cell, then pressing ENTER, typing in the corresponding number, and pressing ENTER again to confirm. The list should automatically scale as you add more data.

sat1 mode 89 000 SAT Test Prep #1: Mean, Mode, and Median on the TI 83 Plus, TI 84 Plus, and TI 89

After you are finished entering data, press F4 ENTER to select 1-Var Stats. Type list1 into the “List:” field and press ENTER ENTER to confirm.

sat1 mode 89 001 SAT Test Prep #1: Mean, Mode, and Median on the TI 83 Plus, TI 84 Plus, and TI 89

Your calculator will then display the 1-Var Stats screen, which displays a wide range of information about your set of data. The mean is denoted by x bar and the median as MedX, which can be reached by pressing .

sat1 mode 89 002 SAT Test Prep #1: Mean, Mode, and Median on the TI 83 Plus, TI 84 Plus, and TI 89

As on the TI-83 Plus and TI-84 Plus, there is no built-in mode function on the TI-89. We’ve created a mode program for the TI-89 here.

To use this program, press 2nd - to get to the VAR-LINK menu, select the “mode” program using the arrow buttons, and finally press ENTER to paste the function to your home screen. Then type list1 and press ) to add a closing parenthesis to the function. Alternately, you can just type mode(list1) into your home screen manually. Press ENTER to evaluate.

sat1 mode 89 003 SAT Test Prep #1: Mean, Mode, and Median on the TI 83 Plus, TI 84 Plus, and TI 89

The program outputs the mode of your set of data and the size of your data set.

sat1 mode 89 004 SAT Test Prep #1: Mean, Mode, and Median on the TI 83 Plus, TI 84 Plus, and TI 89

You can also enter the data as a list in the program. To do this, type “mode(“, press 2nd ( to enter a bracket, and then enter your data separated by commas, add a closing bracket by pressing 2nd ), then press ) ENTER to complete the expression and evaluate.


5 Responses to SAT Test Prep #1: Mean, Mode, and Median on the TI-83 Plus, TI-84 Plus, and TI-89

  1. Tiffany Grard

    Thank you this was very helpful…

  2. John Fox

    Hello! Great tutorial, very appreciated. However, when I follow the instructions for mean on my ti-83 plus, it does not take me back to the home screen and show “mean(L1″ at the home screen

  3. Caroline

    This is a great website! I tried downloading your program to my TI-84 Plus, but it said that it cannot open because I do not have the right program to do so. Do you know of a good program do this with? Also could you please write the steps for downloading the program to your calculator?

    Thank you

  4. Beta

    Thank you, very helpful.

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