Calculate mean, median, mode, and range
Mean, median, mode, and range are four different ways to understand a set of data. They help us find the 'average', the 'middle', the 'most frequent', and the 'spread' of the numbers. Let's dig into data!
Concept
These four terms are key measures in statistics that help us summarize and understand data sets. **1. Mean (The Average)** The mean is what most people think of as the "average." * **How to find it:** 1. **Add** up all the numbers in the data set. 2. **Divide** by the count of how many numbers there are. * **Example:** For the set {2, 2, 4, 8} * Add: 2 + 2 + 4 + 8 = 16 * Divide: There are 4 numbers, so 16 ÷ 4 = 4. * The **mean** is 4. **2. Median (The Middle)** The median is the middle number in an **ordered** data set. * **How to find it:** 1. Put the numbers in order from least to greatest. 2. Find the number exactly in the middle. * If there are two middle numbers (in an even set), the median is the average of those two. * **Example:** For {2, 8, 4, 2} -> Order it first: {2, 2, 4, 8} * The two middle numbers are 2 and 4. * Find their average: (2 + 4) ÷ 2 = 3. * The **median** is 3. **3. Mode (The Most Frequent)** The mode is the number that appears most often in a data set. * **How to find it:** Look for the number that repeats the most. * **Example:** For {2, 2, 4, 8} * The number 2 appears twice, more than any other number. * The **mode** is 2. * A data set can have one mode, more than one mode, or no mode at all. **4. Range (The Spread)** The range tells you how spread out the data is. * **How to find it:** Subtract the smallest number from the largest number. * **Example:** For {2, 2, 4, 8} * Largest: 8 * Smallest: 2 * Subtract: 8 - 2 = 6. * The **range** is 6. **Key Idea:** * **Mean:** The "fair share" value. * **Median:** The "middle" value. * **Mode:** The "most popular" value. * **Range:** The "spread" of the values.
Try it
Practice with data sets! For each data set, find the mean, median, mode, and range. **Data Set 1: {5, 10, 5, 15, 10, 5}** 1. Mean: 2. Median: 3. Mode: 4. Range: **Data Set 2: {7, 2, 9, 4, 8}** 5. Mean: 6. Median: 7. Mode: 8. Range: **Word Problems:** 9. Your test scores are 85, 90, 88, 92, and 85. What is your mean score? What is the mode? 10. The daily temperatures for a week were 65°F, 68°F, 72°F, 70°F, 68°F, 71°F, and 67°F. Find the median temperature and the range. **Challenge Problems:** 11. A data set has a mean of 10 and contains the numbers 8, 12, and 9. What is the missing fourth number? 12. Create a set of 5 numbers where the mean, median, and mode are all 7.