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Sagot :
The given data are 20, 23, 18, 4, 17, 21, 15, and 25
Arrange them at first from smallest to greatest
4, 15, 17, 18, 20, 21, 23, 25
The range is the difference between the greatest and the smallest numbers
Since the smallest number is 4 and the greatest number is 25, then
[tex]\begin{gathered} R=25-4 \\ R=21 \end{gathered}[/tex]The data vary by a range of 21 calls
To find the interquartile range we have the find the median
The median is the middle number
Since we have 8 numbers, then the median will be the average of the 4th and the 5th numbers
Since the 4th number is 18 and the 5th number is 20, then the median is their sum divided by 2
[tex]\begin{gathered} IQ2=\frac{18+20}{2} \\ IQ2=\frac{38}{2} \\ IQ2=19 \end{gathered}[/tex]The middle half of the data is 19 calls
Let us find IQ1 and IQ3
IQ1 is the median of the first 4 numbers
Since the first four numbers are 4, 15, 17, 18, then
[tex]\begin{gathered} IQ1=\frac{15+17}{2} \\ IQ1=\frac{32}{2} \\ IQ1=16 \end{gathered}[/tex]IQ3 is the median of the last 4 numbers
Since the last four numbers are 20, 21, 23, 25, then
[tex]\begin{gathered} IQ3=\frac{21+23}{2} \\ IQ3=\frac{44}{2} \\ IQ3=22 \end{gathered}[/tex]Then the interquartile range is
[tex]\begin{gathered} \text{IQR}=IQ3-IQ1 \\ \text{IQR}=22-16 \\ \text{IQR}=6 \end{gathered}[/tex]The interquartile range is 6 calls
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