SME
Grade 6 Math · Problem type
Box plots
Use this for “What is the interquartile range?” from a box plot.
Chart
The middle half of the data runs from 5 to 11, a width of 6.
Half the values are at or below the median, 8.
This is an example. Type your own values to start a new problem.
Minimum
example
Lower quartile
example
Median
example
Upper quartile
example
Maximum
example
Range
calculated
Interquartile range
calculated
Formulas
15 − 2 = 13
Maximum − minimum = range
11 − 5 = 6
Upper quartile − lower quartile = interquartile range
Assumptions
•
The five numbers are in order: minimum, lower quartile, median, upper quartile, maximum.
•
Each of the four parts holds about a quarter of the data: half the data is below the median.
•
The interquartile range is the width of the box: the middle half of the data.
Step-by-step
WE KNOW
Minimum: 2
Lower quartile: 5
Median: 8
Upper quartile: 11
Maximum: 15
FIND
range, interquartile range
Step 1 · Find range
15 − 2 = ?
Maximum − minimum = range
The range runs from the minimum to the maximum.
Range = 13
Step 2 · Find interquartile range
11 − 5 = ?
Upper quartile − lower quartile = interquartile range
The box runs from the lower quartile to the upper quartile.
Interquartile range = 6
Check
Put the numbers back in. Both sides should match.
15 − 2 = 13 ✓
11 − 5 = 6 ✓
Topic check
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