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Exploring other ways to describe data sets and how spread out the numbers are.
Imagine you're a video game designer. If one pro player scores 1,000,000 points but everyone else scores only 10, does the 'average' score of 100,000 really tell the truth about your game? To see the real story, you need to look deeper than just the average.
The median is the middle value in a list of numbers. Think of it like the 'median' strip in the middle of a highway—it splits the data exactly in half. To find it, you must first perform the most important step: order your numbers from least to greatest. If you have an odd number of values, the median is the one right in the center. If you have an even number, the median is the halfway point (the mean) between the two middle numbers. The median is a 'tough' measure because it isn't easily changed by one or two extremely high or low numbers, which we call outliers.
Find the median of the following test scores: .
1. Order the numbers: . 2. Identify the middle: There are 5 numbers, so the 3rd number is the center. 3. Result: The median is .
Quick Check
What is the very first thing you must do before you can identify the median of a data set?
Answer
You must put the numbers in order from least to greatest.
A group of friends have these shoe sizes: .
1. Find the Mode: The number appears three times, more than any other number. The mode is . 2. Find the Range: The largest size is and the smallest is . 3. Calculate: . 4. Result: The range is .
Quick Check
If a data set is , what are the modes?
Answer
The modes are 10 and 30 (this is called bimodal).
Why do we have so many ways to describe data? Because different situations require different tools! We use the median when there are outliers (extreme values) that would make the average (mean) look misleading. We use the mode when we want to know the most common category, like the most popular pizza topping. We use the range to understand if the data is consistent (small range) or very unpredictable (large range).
Find the median of this data set with an outlier: .
1. Order the numbers: They are already ordered: . 2. Identify the middle: Since there are 6 numbers (even), the middle falls between the 3rd and 4th numbers ( and ). 3. Calculate the middle: Find the number halfway between and : . 4. Analyze: The outlier () didn't change the median much! The median is .
What is the range of the data set: ?
In the set , which number is the mode?
If you add a very large 'outlier' to a data set, the median will usually change more than the mean.
Review Tomorrow
In 24 hours, try to explain to a friend why a real estate agent might use the 'median' house price instead of the 'average' house price.
Practice Activity
Find a handful of coins in your house. List the years they were minted, then calculate the median year, the mode, and the range of the ages of your coins!