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

banganX 2021-11-06 Answered
Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the range and interquartile range.
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## Expert Answer

wornoutwomanC
Answered 2021-11-07 Author has 81 answers
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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