Lesson 10: Choose Appropriate Measures6.DS.6d

I can…

I can choose the best measure of center for a data set based on its shape.

Key words

• Appropriate Measures of Center — A mean, median, or mode chosen because it describes a data set fairly.
• Mean — The average. Add all the numbers, then divide by how many there are.
• Median — The middle number when you put them in order.
• Outlier — A number that is much bigger or smaller than the rest.
• Skewed — When most data sits on one side with a tail on the other.
• Data distribution — How the data looks: where it sits and how spread out it is.
• Variability — How spread out the numbers are.
• Cluster — Values bunched close together in one part of a display.
• Gap — A space on a display where no data values fall.

Steps

1. My data, the top scorer's points: 22, 24, 20, 25, 23, 21, 58. I notice 58 is much bigger than the rest, so it is an outlier.
2. Mean: 22 + 24 + 20 + 25 + 23 + 21 + 58 = 193, then 193 ÷ 7 ≈ 27.6.
3. Median: in order they are 20, 21, 22, 23, 24, 25, 58. The middle (4th) value is 23.
4. The mean (27.6) is higher than 6 of the 7 games because 58 pulled it up. So the median (23) better shows a typical game.

Try it

Six friends timed their trips to school in minutes: 12, 10, 14, 11, 13, 60. Which measure should they use to describe a typical trip time?

Check your answer

Median, because 60 is an outlier

The value 60 is an outlier. The mean (120 ÷ 6 = 20 minutes) is pulled up by 60 and is higher than five of the six trip times. The median (12.5 minutes) stays close to the typical values, so it is the better measure of center.

Sentence starter

I know ___ because ___.

Goal: I can explain my choice using the words mean, median, outlier, and skewed.