Finding the interquartile range (IQR) on a TI-84 takes about 30 seconds once your data is entered. The calculator doesn’t display the IQR directly, but it gives you Q1 and Q3 through the 1-Var Stats function. You subtract Q1 from Q3, and that’s your IQR.
Enter Your Data Into a List
Press [STAT] then [1] to open the list editor. This brings up columns labeled L1, L2, and so on. Type each data value into L1, pressing [ENTER] after each number to move to the next row. If there’s old data in L1, arrow up to highlight the L1 header, press [CLEAR], then [ENTER] to wipe the column before you start.
If your data comes as a frequency table (for example, the value 5 appears 3 times, the value 8 appears 7 times), enter the data values in L1 and the corresponding frequencies in L2. This saves you from typing the same number over and over.
Run 1-Var Stats
Press [STAT], then use the right arrow key to move to the CALC menu. Select 1:1-Var Stats and press [ENTER]. The calculator will ask which list to use. Leave it set to L1. If you entered frequency data in L2, scroll down to the FreqList field, press [2nd] then [2] to select L2. Press [ENTER] to run the calculation.
The first screen of results shows the mean, sum, sum of squares, standard deviation, and the number of data points. The quartile values aren’t on this screen. Press the down arrow key to scroll past these results. Near the bottom you’ll find five values listed in order:
- minX: the smallest value in your data set
- Q1: the first quartile (25th percentile)
- Med: the median (50th percentile)
- Q3: the third quartile (75th percentile)
- maxX: the largest value in your data set
Write down Q1 and Q3. These are the two numbers you need.
Calculate the IQR
The IQR is simply Q3 minus Q1. You can do this subtraction on the home screen, on paper, or in your head. For example, if Q1 is 12 and Q3 is 27, your IQR is 27 minus 12, which equals 15. The IQR tells you the spread of the middle 50% of your data, so in this case the middle half of your values spans a range of 15.
If you want to keep things on the calculator, press [2nd] then [QUIT] to return to the home screen, type the subtraction, and press [ENTER].
Verify With a Box Plot
A box plot is a quick visual check that your quartile values make sense. The left and right edges of the box represent Q1 and Q3, so the width of the box corresponds to the IQR.
Press [2nd] [STAT PLOT] then [1] to open Plot1. Press [ENTER] to turn the plot on. For the graph type, arrow right to select the box plot icon (the fourth option in the row). Make sure Xlist is set to L1 and Freq is set to 1. Press [ZOOM], select 9:ZoomStat, and press [ENTER]. The calculator will automatically scale the window and display your box plot. You can press [TRACE] and use the arrow keys to move along the plot, and the calculator will label the exact values of minX, Q1, Med, Q3, and maxX as you go.
If the box looks oddly wide or narrow compared to what you expected, double-check your list for typos. A single mistyped value can shift Q1 or Q3 significantly, especially in small data sets.
Storing Q1 and Q3 for Later Use
The TI-84 doesn’t save the 1-Var Stats output once you navigate away, but you can store Q1 and Q3 into variables if you need them for further calculations (like finding outlier boundaries at Q1 minus 1.5 times IQR and Q3 plus 1.5 times IQR). After running 1-Var Stats, return to the home screen. Press [VARS], choose 5:Statistics, then arrow over to select Q1 or Q3 from the list. You can use these stored values directly in expressions without retyping the numbers.