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Sagot :
Given:
61,65,65,66,72,75,77,79,81,89,92,99.
There are 12 number of data.
Dividing the set into quartiles, each quarter will have 3 terms as
[tex]\mleft\lbrace61,65,65\mright\rbrace,\mleft\lbrace66,72,75\mright\rbrace,\mleft\lbrace77,79,81\mright\rbrace,\mleft\lbrace89,92,99\mright\rbrace.[/tex]We need to find lower Quartile and upper Quartile to compute the interquartile range.
[tex]Lower\text{ Quartile }(Q_1)=\frac{65+66}{2}=65.5[/tex][tex]Upper\text{ Quartile }(Q_3)=\frac{81+89}{2}=85[/tex]The formula interquartile range is
[tex]interquartile\text{ }range=Q_3-Q_1[/tex][tex]\text{ Substitute }Q_1=85\text{ and }Q_3=65.5\text{ in the formula, we get}[/tex][tex]interquartile\text{ }range=85-65.5[/tex][tex]interquartile\text{ }range=19.5[/tex]Hence the interquartile range of the given set is 19.5.
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