Mean, Median, and Mode: Your Toolkit for Describing Data
In 2022, scientists studying Antarctic winter had 365 daily temperature readings — one for each day of the year. Which single number best described them all? That is exactly the problem descriptive statistics was invented to solve: turning a big messy pile of numbers into a few clear ones.
What You Will Learn
By the end of this lesson you will be able to: - Calculate the mean (average) of a set of numbers - Find the median and mode of a data set - Calculate the range of a data set - Decide which measure best describes a given situation
What Are Descriptive Statistics?
Descriptive statistics are numbers that summarize a data set. Instead of showing someone all 365 temperature readings, you give them one or two numbers that capture the big picture. The four most important measures are: - Mean: the arithmetic average - Median: the middle value when data is sorted - Mode: the most common value - Range: the distance from the lowest to the highest value
The Mean: Finding the Average
The mean is the most common type of average. You calculate it in two steps: Step 1 — Add all the values together. Step 2 — Divide by how many values there are. Example: Five students scored 72, 85, 90, 68, and 100 on a math test. Step 1: 72 + 85 + 90 + 68 + 100 = 415 Step 2: 415 divided by 5 = 83 The mean score is 83. That one number represents the whole group's performance.
Imagine four friends earn $30,000 a year each, and one friend earns $1,000,000. The mean income is ($30,000 times 4 plus $1,000,000) divided by 5 = $224,000. But most people in the group earn far less than $224,000! In cases with extreme outliers, the median gives a more honest picture.
Median and Mode
THE MEDIAN is the middle value when data is arranged from smallest to largest. Example with 5 values — Test scores in order: 68, 72, 85, 90, 100 The middle value is 85 — that is the median. With an even number of values, average the two middle ones. Scores: 68, 72, 85, 90 — the two middle values are 72 and 85, so the median = (72 + 85) divided by 2 = 78.5 THE MODE is the value that appears most often. Example: 5, 7, 7, 8, 9, 10, 10, 10 — the mode is 10 because it appears 3 times. A data set can have more than one mode, or no mode at all if every value appears just once.
Range: How Spread Out Is the Data?
The range tells you how spread out your data is. Range = Largest value minus Smallest value Example: Temperatures recorded for a week: 55, 60, 47, 72, 68, 50, 63 degrees Fahrenheit Largest: 72 Smallest: 47 Range: 72 minus 47 = 25 degrees A small range means the data points are close together. A large range means there is a lot of variation.
A basketball player scored 18, 22, 15, 22, and 13 points in five games. What is the mean score?
When is the median a better measure than the mean?
Describe Your Group's Shoe Sizes
1. Ask at least 8 people — classmates, family members, or friends — for their shoe sizes. Record them in a list. 2. Arrange the shoe sizes from smallest to largest. 3. Calculate the MEAN: add all shoe sizes together, then divide by the count. Round to one decimal place. 4. Find the MEDIAN: identify the middle value (or average the two middle values if you have an even count). 5. Find the MODE: which shoe size appears most often? 6. Calculate the RANGE: largest size minus smallest size. 7. Write one sentence explaining which measure — mean, median, or mode — you think best describes your group's typical shoe size and why you chose it.
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