How To Make A Box Plot On Ti 84

Creating box plots on a TI-84 calculator is a straightforward process that can significantly enhance your data analysis capabilities. A box plot, also known as a box-and-whisker plot, is a visual representation of data that displays the median, quartiles, and outliers, offering a comprehensive snapshot of the distribution. The TI-84 series, popular among students and professionals, offers built-in functionalities to generate these plots quickly. This guide will walk you through the steps, ensuring you master creating box plots on your TI-84 calculator.

Understanding Box Plots

Before diving into the how-to, it's crucial to understand what a box plot represents. Box plots are useful because they:

• Show the median, indicating the center of the data.
• Display the quartiles (Q1 and Q3), representing the 25th and 75th percentiles, respectively.
• Identify the interquartile range (IQR), which is the range between Q1 and Q3.
• Highlight outliers, which are data points significantly different from the rest of the data.
• Illustrate the spread and skewness of the data.

A typical box plot consists of:

• The Box: Drawn from Q1 to Q3.
• The Median Line: A line inside the box representing the median.
• The Whiskers: Lines extending from the box to the farthest non-outlier data points.
• Outliers: Individual points beyond the whiskers.

Step-by-Step Guide to Creating a Box Plot on TI-84

Step 1: Entering Data

The first step is to input your data into the calculator.

1. Turn on your TI-84 calculator.

2. Press the STAT button. This button is usually located in the middle of the top row of buttons.

3. Select 1:Edit... by pressing ENTER. This opens the list editor where you can enter your data.

4. Enter your data into one of the lists (e.g., L1, L2, L3). If there's existing data in the list, clear it by highlighting the list name (e.g., L1), pressing CLEAR, and then pressing ENTER.

5. Input each data point followed by ENTER.

   Example:

   Let's say you want to create a box plot for the following data set:

   • 12, 15, 18, 20, 22, 25, 28, 30, 32, 35, 38, 40, 42, 45, 48

   Enter these numbers into list L1.

Step 2: Setting Up the Stat Plot

Once your data is entered, you need to set up the stat plot to create the box plot.

1. Press 2nd and then Y= (STAT PLOT) to access the Stat Plot menu.

2. Choose one of the plots (Plot1, Plot2, or Plot3) by pressing 1, 2, or 3, and then press ENTER.

3. Turn the plot On by highlighting "On" and pressing ENTER.

4. Select the Box Plot type. There are two box plot options:

   • The first box plot icon (with outliers shown as individual points) is used when you want the calculator to identify and display outliers.
   • The second box plot icon (without outliers as individual points) shows the minimum and maximum values as the ends of the whiskers.

   Choose the one that suits your needs. For most purposes, the box plot with outliers is preferable.

5. Set the Xlist to the list where you entered your data (e.g., L1). If your data is in L1, ensure "Xlist" says "L1". To enter L1, press 2nd and then 1.

6. Ensure the Freq is set to 1. This indicates each data point has a frequency of one.

Step 3: Displaying the Box Plot

With the data entered and the stat plot set up, you can now display the box plot.

1. Press ZOOM.

2. Scroll down to 9:ZoomStat and press ENTER. ZoomStat automatically adjusts the window settings to fit your data, ensuring the box plot is displayed correctly.

   Your box plot should now be visible on the screen.

Step 4: Analyzing the Box Plot

Once the box plot is displayed, you can analyze it by reading the key values.

1. Press TRACE. This activates the trace function, allowing you to move along the box plot and read the values.
2. Use the left and right arrow keys to move along the plot. The calculator will display the following values:
   • minX: The minimum value in the data set.
   • Q1: The first quartile (25th percentile).
   • Med: The median (50th percentile).
   • Q3: The third quartile (75th percentile).
   • maxX: The maximum value in the data set.
   • Outliers: If there are any outliers, the calculator will display their values as you move to them.

Additional Tips and Tricks

• Adjusting the Window Settings: If you want to customize the viewing window, press WINDOW. Here, you can manually adjust the Xmin, Xmax, Ymin, and Ymax values. For a box plot, it’s generally best to leave the Y values at their default settings.
• Clearing Stat Plots: If you’re having trouble displaying the box plot, ensure there are no other stat plots turned on that might be interfering. Go to STAT PLOT (2nd + Y=) and turn off any other plots that are active.
• Frequency Lists: If your data includes frequencies (i.e., some data points occur more than once), you can enter the frequencies into another list (e.g., L2) and specify this list in the "Freq" setting of the stat plot.
• Error Messages: If you encounter an error message, double-check that your data is entered correctly and that the stat plot settings are accurate. Common errors include mismatched list sizes or incorrect plot settings.

Examples

Let’s walk through a few examples to solidify your understanding.

Example 1: Simple Data Set

Data Set: 5, 7, 9, 11, 13, 15, 17, 19, 21

1. Enter the data into L1.
2. Go to STAT PLOT and turn on Plot1.
3. Select the box plot type with outliers.
4. Set Xlist to L1 and Freq to 1.
5. Press ZOOM and select ZoomStat.
6. Analyze the box plot using TRACE.

Example 2: Data Set with Outliers

Data Set: 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 50

1. Enter the data into L1.
2. Go to STAT PLOT and turn on Plot1.
3. Select the box plot type with outliers.
4. Set Xlist to L1 and Freq to 1.
5. Press ZOOM and select ZoomStat.
6. Analyze the box plot using TRACE. You should see an outlier at 50.

Example 3: Using Frequency Lists

Data Set:

• Value: 1, 2, 3, 4, 5
• Frequency: 3, 5, 7, 2, 1

1. Enter the values (1, 2, 3, 4, 5) into L1.
2. Enter the frequencies (3, 5, 7, 2, 1) into L2.
3. Go to STAT PLOT and turn on Plot1.
4. Select the box plot type with outliers.
5. Set Xlist to L1 and Freq to L2. (To enter L2, press 2nd and then 2).
6. Press ZOOM and select ZoomStat.
7. Analyze the box plot using TRACE.

Common Mistakes to Avoid

• Incorrect List Selection: Make sure you’ve selected the correct list where your data is stored in the Stat Plot settings.
• Leaving Other Plots On: Ensure that only the plot you want to display is turned on. Multiple active plots can cause confusion.
• Forgetting to Clear Old Data: Always clear the list before entering new data to avoid mixing old and new data points.
• Incorrect Frequency Settings: If you’re using frequency lists, double-check that the frequencies are correctly entered and linked to the correct data values.
• Misinterpreting Outliers: Understand that outliers are data points that are significantly different but not necessarily errors. They should be investigated further but not automatically discarded.

Advanced Applications

Once you’re comfortable creating basic box plots, you can explore more advanced applications.

• Comparing Multiple Data Sets: Create multiple box plots on the same screen to compare different data sets. To do this, enter each data set into a separate list (e.g., L1, L2, L3) and set up multiple stat plots (Plot1, Plot2, Plot3), each referencing a different list.
• Using Box Plots in Hypothesis Testing: Box plots can provide a quick visual check of data distribution, which can be helpful in preliminary hypothesis testing.
• Analyzing Changes Over Time: Create box plots for data collected at different time points to visualize how the distribution changes over time.

The Mathematical Foundation of Box Plots

Understanding the math behind box plots can deepen your appreciation for their utility. Here's a breakdown:

• Median (Q2): The middle value of the dataset when it's sorted. If there is an even number of data points, the median is the average of the two middle values.
• First Quartile (Q1): The median of the lower half of the dataset. It represents the 25th percentile.
• Third Quartile (Q3): The median of the upper half of the dataset. It represents the 75th percentile.
• Interquartile Range (IQR): The range between the first and third quartiles (IQR = Q3 - Q1). It measures the spread of the middle 50% of the data.
• Outliers: Data points that fall significantly outside the main distribution. They are typically defined as:
  • Values less than Q1 - 1.5 * IQR
  • Values greater than Q3 + 1.5 * IQR
• Whiskers: Lines extending from the box to the farthest data points that are not outliers.

Interpreting Skewness and Symmetry

Box plots can reveal the skewness and symmetry of the data distribution:

• Symmetric Distribution: If the median is in the middle of the box and the whiskers are roughly equal in length, the distribution is approximately symmetric.
• Right-Skewed (Positive Skew): If the median is closer to the bottom of the box and the right whisker is longer, the distribution is right-skewed. This indicates that there are more higher values in the dataset.
• Left-Skewed (Negative Skew): If the median is closer to the top of the box and the left whisker is longer, the distribution is left-skewed. This indicates that there are more lower values in the dataset.

Practical Applications of Box Plots

Box plots are used across various fields to analyze data and make informed decisions. Here are a few examples:

• Finance: Comparing the distribution of stock prices, identifying outliers in financial data, and assessing risk.
• Healthcare: Analyzing patient data, comparing treatment outcomes, and identifying unusual health indicators.
• Education: Evaluating student performance, comparing test scores across different groups, and identifying students who may need additional support.
• Engineering: Analyzing product quality, comparing the performance of different designs, and identifying potential defects.
• Environmental Science: Analyzing environmental data, comparing pollution levels across different locations, and identifying unusual environmental events.

Conclusion

Creating box plots on a TI-84 calculator is a valuable skill for anyone working with data. By following this comprehensive guide, you can effectively enter data, set up stat plots, display box plots, and analyze the results. Understanding the mathematical foundation and practical applications of box plots will further enhance your ability to interpret and use them in various fields. Whether you’re a student, a professional, or simply someone interested in data analysis, mastering box plots on your TI-84 calculator will undoubtedly prove to be a valuable asset. Embrace these techniques, and you'll find your data analysis capabilities significantly enhanced. Remember to practice regularly, and soon, creating and interpreting box plots will become second nature.