Unlocking Data: Your Step-by-Step Guide to Using the TI-84 for Statistics

Unlocking Data: Your Step-by-Step Guide to Using the TI-84 for Statistics The TI-84 graphing calculator is a powerhouse for statistics, capable of handling everything from calculating a simple average to running complex hypothesis tests. If you’re taking a statistics class, learning to wield this tool effectively can save you hours of manual calculation and help you visualize data in powerful ways.

This guide will walk you through the entire process, from entering your data to interpreting the results, using a clear example.

The Example Dataset

Let’s use a simple dataset throughout this guide. Imagine we recorded the test scores for 10 students:
85, 92, 78, 90, 88, 95, 83, 80, 87, 91

Our goals:

1. Enter this data.
2. Calculate descriptive statistics (mean, median, standard deviation, etc.).
3. Create a box plot and a histogram to visualize the data.
4. Perform a linear regression (if we had a second variable).

Entering Your Data into Lists

All statistical work on the TI-84 begins with entering your data into lists.

1. Press the STAT button. You’ll see a menu like EDIT, CALC, TESTS.
2. Select 1:Edit... by pressing ENTER. This will open your list screen, typically labeled L1, L2, L3, etc.
3. Enter your data. If L1 has existing data, arrow up to highlight L1, press CLEAR, then arrow down to start entering numbers.
   • Type the first number (85) and press ENTER.
   • Type the next number (92), press ENTER.
   • Continue until all 10 scores are entered into L1.
4. (Optional) Naming a List: To keep things organized, you can name your list “SCORES”.
   • Arrow over to the top of the column where it says L1.
   • Press CLEAR to delete the L1.
   • Type S, C, O, R, E, S (use the ALPHA key or the green letter keys above each button).
   • Press ENTER.

Your data is now loaded and ready for analysis.

Calculating Descriptive Statistics

You don’t need to memorize formulas; the calculator can compute all the basic summary statistics at once.

1. Press STAT again.
2. Arrow over to the CALC menu.
3. Select 1:1-Var Stats (1-Variable Statistics). This is for analyzing a single dataset.
4. Now, you need to tell the calculator which list your data is in.
   • If you used the default L1, simply press ENTER.
   • If you used a different list, press 2ND and then the number of the list (e.g., 2ND 2 for L2). Or, you can press 2ND 1 to get the L1 token.
5. The screen will say 1-Var Stats L1. Press ENTER again.

A screen full of numbers will appear! Here’s what they all mean:

• x̄ (x-bar): The mean of your data. (For our data, it should be ~86.9).
• Σx: The sum of all the data points.
• Σx²: The sum of all the data points squared.
• Sx: The sample standard deviation (use this if your data is from a sample). This measures spread.
• σx: The population standard deviation (use this if your data is from an entire population).
• n: The number of data points.
• minX: The smallest value in the dataset.
• Q1: The first quartile (the median of the lower half).
• Med: The median.
• Q3: The third quartile (the median of the upper half).
• maxX: The largest value in the dataset.

To see all these values, use the up and down arrow keys to scroll through the list.

Creating Visualizations (Plots)

Seeing your data is just as important as calculating numbers. Let’s make two common graphs.

Creating a Box Plot (Box-and-Whisker Plot)

1. Press 2ND Y= (which is the STAT PLOT button).
2. Select 1:Plot1... and press ENTER.
3. Turn the plot On.
4. Arrow down to Type: and select the box plot icon (the middle one in the second row).
5. Ensure Xlist: is set to L1 (or wherever your data is). Freq: should be 1.
6. Now, press ZOOM and select 9:ZoomStat. This automatically sets the window to perfectly fit your data.

You will now see a box plot representing the five-number summary (min, Q1, Med, Q3, max) of your test scores.

Creating a Histogram

1. Go back to 2ND Y= > STAT PLOT.
2. Select 2:Plot2..., turn it On.
3. Change the Type: to the histogram icon (the third one in the first row).
4. Ensure Xlist: is L1 and Freq: is 1.
5. Press ZOOM 9:ZoomStat again.

The calculator will automatically create bins (ranges) for your data. You can adjust the bin width and starting point by pressing the WINDOW button after you see the graph.

To turn off a plot, go back to STAT PLOT and set it to Off.

Performing Linear Regression (With Two Variables)

What if you had a second variable? For example, hours studied vs. test score.

• L1: Hours Studied: 2, 5, 1, 4, 3, 6, 2, 3, 4, 5
• L2: Test Score: 85, 92, 78, 90, 88, 95, 83, 80, 87, 91

1. Enter the “Hours Studied” data into L1 and the “Test Score” data into L2. Make sure the data pairs line up!
2. Press STAT, arrow over to CALC.
3. Select 4:LinReg(ax+b). This finds the line of best fit.
4. You need to tell it where your data is. The format is LinReg(ax+b) Xlist, Ylist
   • To do this easily, press 2ND 1 (for L1), then , (the comma button), then 2ND 2 (for L2).
5. The command should look like: LinReg(ax+b) L1,L2
6. Press ENTER.

The calculator will display the values for:

• a: The slope of the regression line.
• b: The y-intercept.
• r² and r: The coefficients of determination and correlation, which tell you the strength and direction of the relationship.

You can now write the equation of the line: y = ax + b

To graph the scatter plot and regression line together:

1. Set up a STAT PLOT for a scatter plot (the first icon) using L1 and L2.
2. Press Y=. Arrow up to a blank function and press VARS, then 5:Statistics..., arrow over to EQ, and select 1:RegEQ. This will paste the regression equation you just calculated directly into Y1.
3. Press ZOOM 9:ZoomStat. You will see your scatter plot with the line of best fit drawn through it.

Pro Tips and Final Advice

• Clearing Data: Always clear lists (STAT > Edit... > arrow up to list name > CLEAR > ENTER) before entering new data to avoid mixing datasets.
• Double-Check Entries: A single data entry error can throw off all your calculations. Always review your lists.
• Understand the Context: The calculator gives you numbers, but you must interpret them. Knowing that Sx is your sample standard deviation and what it means is your job.
• Practice: The more you use these functions, the more intuitive they become. Use this guide to walk through the steps with your own homework problems.

The TI-84 is an incredible partner for statistics. By mastering these fundamental steps, you transform it from a simple calculator into a powerful data analysis engine, ready to tackle any problem your course throws at it.

Frequently Asked Questions (FAQs)

Q1: How do I clear data from a list or reset my calculator’s statistics functions?

• A: To clear a single list, go to STAT > 1:Edit..., use the arrow keys to highlight the list name (e.g., L1), press CLEAR, and then press ENTER. Do not press DEL, as that will delete the entire list column. To perform a more complete reset, press 2ND + (MEM) and select 7:Reset.... Then choose 1:All Ram... and 2:Reset. Warning: This will erase all data and stored values, not just in stats lists.

Q2: What’s the difference between Sx and σx in the 1-Var Stats results? Which one should I use?

• A: This is a crucial distinction:
  • Sx is the sample standard deviation. Use this when your data represents a sample taken from a larger population. This is the most common choice in introductory statistics courses.
  • σx is the population standard deviation. Use this only if your dataset includes every single member of the population you are studying.
  • When in doubt, use Sx.

Q3: I entered my data correctly, but when I try to create a plot, the graph is blank or looks wrong. What happened?

• A: This is almost always one of two issues:
  1. The Plot is not turned on: Go to 2ND Y= (STAT PLOT) and ensure the plot you are using (Plot1, Plot2, etc.) is set to On.
  2. The Window needs adjusting: After turning on the plot, always press ZOOM and select 9:ZoomStat. This command automatically sets the X and Y ranges to perfectly fit your specific data. If you manually set the window (WINDOW button), your data might be outside the viewing area.

Q4: How do I calculate standard deviation or mean by itself without getting all the 1-Var Stats?

• A: You can access these values directly after running 1-Var Stats.
  • Press VARS to access the variables menu.
  • Select 5:Statistics...
  • Navigate to the XY submenu. Here you will find all the calculated values (like X̄ for mean, Sx for sample standard deviation, σx for population standard deviation, n, etc.). You can use these in other calculations.

Q5: Can I perform a linear regression if my data is not in L1 and L2?

• A: Absolutely. When you choose 4:LinReg(ax+b), you can specify any two lists. The full syntax is LinReg(ax+b) [Xlist], [Ylist]. For example, if your x-data is in L3 and your y-data is in L4, you would enter: LinReg(ax+b) L3,L4.

Q6: What do the r and r² values mean in linear regression?

• A: These values measure the strength and direction of the linear relationship.
  • r (correlation coefficient): A value between -1 and 1.
    • r = 1: Perfect positive linear relationship.
    • r = -1: Perfect negative linear relationship.
    • r = 0: No linear relationship.
  • r² (coefficient of determination): A value between 0 and 1. It tells you what percentage of the change in the y-variable can be explained by the change in the x-variable. An r² of 0.85 means 85% of the variation in y is explained by x.

Q7: How do I add a regression line to my scatter plot?

• A: There are two main ways:
  1. Automatic Paste: After calculating the regression (LinReg(ax+b)), press Y=, arrow up to a blank function (e.g., Y1), press VARS, select 5:Statistics > EQ > 1:RegEQ. This will paste the full equation.
  2. Manual Entry: Simply type the equation manually into the Y= screen using the a and b values provided by the LinReg output. The format will be Y1 = a*X + b.

Q8: My histogram looks chunky or has weird bars. How can I change the bin width?

• A: The calculator automatically chooses bin widths based on your data. To change them:
  1. Press WINDOW after you have graphed the histogram.
  2. You will see Xmin, Xmax, and Xscl.
  3. Xscl controls the bin width. Adjust this number to make the bars wider (larger number) or narrower (smaller number).
  4. Press GRAPH again to see the updated histogram. You may need to adjust Xmin and Xmax accordingly.