LAB 6: Graphing Calculator: Calculating 1- and 2-Variable Statistical Data

New Concept

A graphing calculator can be used to analyze data sets of 1 and 2 variables.

Why it matters

Algebra is the language we use to describe relationships, and statistics allows us to uncover those relationships in real-world data. Mastering this tool frees you from tedious calculation, empowering you to analyze complex patterns like a professional data scientist.

What’s next

Next, you’ll master the calculator's statistical functions and learn to visualize data with box-and-whisker plots.

To analyze a single list of data, use the 1-Var Stats command. This function calculates key statistical values for the data set entered in a list, like L1. Access this feature from the menu by pressing STAT, navigating to the CALC menu, and selecting 1: 1-Var Stats.

Enter {-12, 4, 13, 21, 30} into list L1. Then, press STAT > CALC > 1: 1-Var Stats and input L1. The calculator displays the mean $\bar{x} = 11.2$, the sum $\Sigma x = 56$, and the median Med=13.
For a list of temperatures {68, 75, 72, 65, 80} in L1, using 1-Var Stats quickly provides the average temperature $\bar{x} = 72$ and shows the temperature range.

Think of your calculator as a data detective! Just give it a list of numbers, like your video game high scores, and it instantly reveals the secrets. It finds the average score, the total of all scores, and other cool stats, saving you from a mountain of manual calculations. It’s like having a math superpower in your pocket!

To analyze paired data sets, use the 2-Var Stats command. This function analyzes data in two lists (e.g., L1 and L2) simultaneously. A key statistic calculated is $\Sigma xy$, which represents the sum of the products of each corresponding pair of data values from the two lists.

Enter {-12, 4, 13, 21, 30} into L1 and {5, 6, 16, 21, 23} into L2. Use STAT > CALC > 2: 2-Var Stats L1, L2 to find $\Sigma xy = 1301$.
To analyze hours worked (L1) and tips earned (L2), enter {4, 5, 8} and {20, 30, 50} as dollars. 2-Var Stats calculates $\Sigma xy = 630$ to help see the connection.

This feature is like a data matchmaker! It takes two lists of numbers that are related, like hours you study and your grade on a test, and sees how they connect. The calculator does all the heavy lifting of pairing them up and calculating their combined stats, especially the $\Sigma xy$, to reveal their relationship.

To visualize a single data set, create a box-and-whisker plot. In the STAT PLOT menu, turn a plot on, select the box-plot symbol as the type, and assign a data list to the Xlist. Use the ZoomStat command to automatically adjust the window and display the plot on the graph.

Enter {5, 6, 16, 21, 23} into L2. Go to STAT PLOT, turn on Plot1, select the box plot type for Xlist L2, and press ZOOM > 9: ZoomStat to see the graph.
For a data set of student ages {12, 13, 13, 14, 16} in L1, creating a box-and-whisker plot with ZoomStat will instantly show the median age is 13.

A box-and-whisker plot is a visual snapshot of your data's story. It draws a picture showing the lowest and highest values (the whiskers) and where the middle chunk of your data lies (the box). It’s a super-fast way to see if your numbers are bunched up or spread far apart, without any complicated math.