By Michael Carroll
Updated Aug 30, 2022

Covariance measures the degree to which two ordered data sets vary together. While the TI‑83 can store data lists and run basic statistics, it does not have a dedicated command for covariance. The following steps guide you through calculating covariance using the calculator’s existing functions.

Step 1 – Prepare Your Data Lists

Press STAT, then 1 to open the Stat List Editor. Use the arrow keys to locate two empty lists (e.g., L1 and L2). If you prefer to clear the default lists, press STAT, then 4 (ClrList), then 2nd 1 , 2nd 2, and finally ENTER. Return to the editor by pressing STAT and then 1 again.

Step 2 – Enter Your Data

Highlight the first cell of a list and input a number, then press ENTER. The next cell will be automatically selected. Continue this process until the list is complete. Move to the next list and repeat the procedure. Ensure both lists contain the same number of entries, as each pair will be treated together in the covariance calculation.

Step 3 – Compute Two‑Variable Statistics

Press STAT, then the right arrow to open the STAT CALC menu, and select 2 for 2‑Var Stats. If you’re using the default lists, simply hit ENTER. Otherwise, type the list names separated by a comma (e.g., 2nd L1, 2nd L2) before pressing ENTER. The calculator will display a suite of statistics, including the sums and means needed for covariance.

Step 4 – Build the Covariance Formula

Press VARS, then 5, the right arrow, and 5 to insert Σxy. Divide by the number of observations: ÷ VARS 5 1 (n). Then subtract the product of the means: - VARS 5 2 VARS 5 5 (which represents ar{x}ar{y}). The full expression should read: (Σxy / n) – (x̄ · ȳ). Press ENTER to display the covariance.

TL;DR (Too Long; Didn’t Read)

If you calculate covariance frequently, consider creating a TI‑83 program to automate the steps. Chapter 16 of the TI‑83 Guidebook explains how to program the calculator. You can also find free software online to transfer programs from a computer to the TI‑83.