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In the data set below, what are the lower quartile, the median, and the upper quartile? $\newline$ $11, 13, 15, 16, 17, 71, 71, 73, 76, 83, 88$ $\newline$ lower quartile = ___ $\newline$ median = _ $\newline$ upper quartile = ___

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Calculate quartiles and interquartile range

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Q. In the data set below, what are the lower quartile, the median, and the upper quartile?

\newline

11, 13, 15, 16, 17, 71, 71, 73, 76, 83, 88

\newline

lower quartile = _____

\newline

median = _____

\newline

upper quartile = _____

Identify the median: Step $1$ : Identify the median of the data set. $\newline$ Data set: $11, 13, 15, 16, 17, 71, 71, 73, 76, 83, 88$ . $\newline$ There are $11$ numbers, so the median is the $6$ th number. $\newline$ Calculation: Median $= 71$ .
Identify the lower quartile: Step $2$ : Identify the lower quartile. $\newline$ For the lower quartile, consider the first half of the data set, excluding the median. $\newline$ First half: $11, 13, 15, 16, 17$ . $\newline$ The lower quartile is the median of these $5$ numbers, which is the $3$ rd number. $\newline$ Calculation: Lower quartile $= 15$ .
Identify the upper quartile: Step $3$ : Identify the upper quartile. $\newline$ For the upper quartile, consider the second half of the data set, excluding the median. $\newline$ Second half: $71, 73, 76, 83, 88$ . $\newline$ The upper quartile is the median of these $5$ numbers, which is the $3$ rd number. $\newline$ Calculation: Upper quartile $= 76$ .

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