What is the interquartile range of the data set: 8, 9, 10, 11, 12?

1 Answer
Jim G.
Jan 15, 2018

#"interquartile range "=3#

Explanation:

#"first find the median and the lower/upper quartiles"#

#"the median is the middle value of the data set "#

#"arrange the data set in ascending order"#

#8color(white)(x)9color(white)(x)color(red)(10)color(white)(x)11color(white)(x)12#

#rArr"the median "=10#

#"the lower quartile is the middle value of the data to the"#
#"left of the median. If there is no exact value then it is the"#
#"average of the values on either side of the middle"#

#"the upper quartile is the middle value of the data to the"#
#"right of the median. If there is no exact value then it is the"#
#"average of the values on either side of the middle"#

#8color(white)(x)color(purple)(uarr)color(white)(x)9color(white)(x)color(red)(10)color(white)(x)11color(white)(x)color(purple)(uarr)color(white)(x)12#

#"lower quartile "(Q_1)=(8+9)/2=8.5#

#"upper quartile "(Q_3)=(11+12)/2=11.5#

#"interquartile range "=Q_3-Q_1=11.5-8.5=3#

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