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

Stuck? Start here. Read the steps, try the problem, then check your answer.

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.

Range and Interquartile Range — Two numbers that describe spread: the range covers all the data, and the interquartile range covers only the middle half.
Range — The distance from the least value to the greatest value, found by subtracting: greatest − least.
Quartile — One of the three values that cut an ordered data set into four equal-sized groups.
Interquartile range — The distance across the middle half of the data, found by subtracting the first quartile from the third: Q3 − Q1.
Variability — How much the values in a data set differ from one another — whether they sit close together or far apart.
Measure of variation — A single number that describes the spread of a whole data set. The range and the IQR are both measures of variation.

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.
Range: I subtract the least value from the greatest. 94 − 68 = 26. The scores span 26 points from end to end.
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.
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.
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.

A box plot has Q1 = 20 and Q3 = 36, with a least value of 10 and a greatest value of 50. What is the IQR, and what does it tell you?

IQR = 16; the middle half of the data spans 16 units

IQR = Q3 − Q1 = 36 − 20 = 16. Because it runs from Q1 to Q3, it describes only the middle half of the values — the width of the box.

I know ___ because ___.

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