Studio Aletheia · The Center for Quantitative Studies
6.DPSR.1.4SC 6th Grade Math
Median, Mode, Range, and IQR
Lesson 11 · New Content, Calculate Center and Spread
You've used median, quartiles, and outliers to describe data before, now it's time to calculate all four key statistics precisely. Today you'll find the median, mode, range, and interquartile range of a data set, step by step.
Learning Targets and Success Criteria
Let's calculate all four statistics on the same data set, so you can see how they fit together.
What I will learn
- I can calculate the median of a numerical data set.
- I can calculate the mode of a numerical data set.
- I can calculate the range of a numerical data set.
- I can calculate the interquartile range of a numerical data set.
What success looks like
- I correctly find the median of an ordered data set, including sets with an even count.
- I correctly identify the mode, or state that there is none.
- I calculate the range by subtracting the least value from the greatest.
- I calculate the interquartile range by subtracting the first quartile from the third quartile.
Calculate the median, mode, range, and interquartile range of a data set.
The words we'll use in today's lesson.
These terms will carry through today's mini-lesson, Data Lab, hands-on activity, journal, and exit challenge, and they'll keep coming back all year.
Median
The middle value of a data set when the values are ordered from least to greatest.
Mode
The value or values that occur most often in a data set.
Range
The difference between the greatest and least values in a data set.
Interquartile Range
The distance between the first quartile and the third quartile, showing the spread of the middle half of a data set.
Where this shows up in the real world.
Thinking like a mathematician is not just a school skill. It's what people get paid to do every day, in jobs you may not have heard of yet.
Four Numbers, One Complete Picture
A data analyst almost never reports just one statistic. Soon you'll see how median, mode, range, and interquartile range work together, center and spread, to describe a data set completely, instead of leaving out half the story.
Four Statistics, One Data Set
Let's calculate all four statistics on the same data set, so you can see how they fit together.
Take the data set: ages of 5 cousins: 6, 8, 8, 10, 12. First, order it, it already is. The medianThe middle value of a data set when the values are ordered from least to greatest. is the middle value, 8. The modeThe value or values that occur most often in a data set. is the value that occurs most often, and 8 appears twice while every other value appears once, so the mode is also 8. The rangeThe difference between the greatest and least values in a data set. is the distance from least to greatest: 12 minus 6 equals 6.
Now for the trickier one. Split the data into a lower half, {6, 8}, and an upper half, {10, 12}. The first quartile is the middle of the lower half: (6 + 8) ÷ 2 = 7. The third quartile is the middle of the upper half: (10 + 12) ÷ 2 = 11. The interquartile rangeThe distance between the first quartile and the third quartile, showing the spread of the middle half of a data set. is the third quartile minus the first quartile: 11 minus 7 equals 4. That single number, 4, tells you how spread out the middle half of the data is, a tighter measure of spread than the range, because it isn't affected by extreme values the way range can be.
Adapted from Studio Aletheia's The Center for Quantitative Studies curriculum library, drawing on mathematical resources and the SC CCR Mathematics Standards.
Materials for the Data Lab.
- A. Statistic Calculation Cards
- B. Ruler
- C. Whiteboard markers
- D. Your Data Journal
- E. A calculator (optional)
Order the data first, then calculate median, mode, range, and interquartile range in that order, every single time.
Four-Statistic Lab
We'll calculate all four statistics together before you tackle a data set on your own.
Calculate All Four Statistics
You'll calculate median, mode, range, and interquartile range for a data set and show every step.
Data Journal Entry
Accountability Checklist
Calculate All Four
Find the median, mode, range, and interquartile range of this data set: 4, 4, 6, 8, 10. Show your work for each statistic.
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