banganX

2021-11-06

Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the range and interquartile range.

wornoutwomanC

Expert

The range is the difference between the largest and the smallest value:
RANGE =20-10=10
The first quartile is the median of the data values below the median (or at 25% of the data):
${Q}_{1}=\frac{10+12}{2}=11$
The third quartline is the median of the data values above the median (or at 75% of the data):
${Q}_{3}=\frac{17+20}{2}=18.5$
The interquartile range IQR is the difference of the third and first quartile:
$IQR={Q}_{3}-{Q}_{1}=18.5-11=7.5$
Results:
RANGE=10
IQR=7.5

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