Lesson 5: Describe Data by Range and Interquartile Range6.DS.3

I can…

I can find the range and the interquartile range of a data set and use them to describe how spread out the data is.

Key words

• Range and Interquartile Range — Two numbers that tell how far apart the data is.
• Range — How far it is from the least to the greatest.
• Quartile — One of three numbers that split data into four equal parts.
• Interquartile range — The distance across the middle half of the data.
• Variability — How far apart the numbers are.
• Measure of variation — One number that tells how far apart the data is.
• Extreme value — The lowest or highest value, far from the rest.

Steps

1. Here are 20 history test scores in order: 68, 70, 73, 74, 75, 76, 77, 80, 82, 83, 84, 85, 86, 86, 88, 88, 90, 90, 93, 94. Ordering them first is what makes every step after this possible.
2. Range: I subtract the least value from the greatest. 94 − 68 = 26. The scores span 26 points from end to end.
3. Now the quartiles. The median splits the 20 scores into two halves of 10. The median is halfway between the 10th and 11th values: (83 + 84) ÷ 2 = 83.5.
4. Q1 is the median of the lower 10 values: halfway between 75 and 76, so Q1 = 75.5. Q3 is the median of the upper 10: halfway between 88 and 88, so Q3 = 88.
5. Interquartile range: IQR = Q3 − Q1 = 88 − 75.5 = 12.5. The middle half of the students' scores differed by only 12.5 points, even though the full range was 26.

Try it

A box plot shows how many minutes students read each night. Q1 = 14 and Q3 = 32. The least value is 6 and the greatest value is 45. What is the IQR, and what does it tell you?

Check your answer

IQR = 18; the middle half of the data spans 18 minutes

IQR = Q3 − Q1 = 32 − 14 = 18. Because it runs from Q1 to Q3, it describes only the middle half of the reading times — the width of the box.

Sentence starter

I know ___ because ___.

Goal: I can explain what the spread of a data set is using the words range, quartile, interquartile range, and vary.