Lesson 3: Describe the Data Using the Median6.DS.4

I can…

I can find the median of a data set and use it to describe what is typical.

Key words

• Describe the Data Using the Median — Using the middle value of the ordered data to say what is typical for the whole set.
• Median — The middle number when you put them in order.
• Mode — The number that shows up most often.
• Outlier — A number that is much bigger or smaller than the rest.
• Data distribution — How the data looks: where it sits and how spread out it is.
• Variability — How spread out the numbers are.

Steps

1. My data set: 2, 4, 4, 6, 9 — five values, already in order. Ordering first is what makes a middle exist at all.
2. With 5 values, the middle is the 3rd one. Counting in from both ends: 2 and 9 pair off, 4 and 6 pair off, and 4 is left alone.
3. So the median is 4. Half the values sit at or below it and half at or above it.
4. Now an even set: 2, 4, 6, 9. There is no single middle, so I take the mean of the two middle values: (4 + 6) ÷ 2 = 5. The median is 5, even though 5 is not in the data.

Try it

Data set: 4, 7, 10, 7, 12. What is the median, and what does it tell you?

Check your answer

7 — a typical value in this set is about 7

Put the values in order first: 4, 7, 7, 10, 12. With five values the middle is the 3rd, so the median is 7 — half the values sit at or below it.

Sentence starter

I know ___ because ___.

Goal: I can explain the median using the words order, middle, typical, and half.