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In the data set below, what are the lower quartile, the median, and the upper quartile? $\newline$ $12, 19, 23, 24, 69, 74, 76, 86, 87, 89, 92$ $\newline$ 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

12, 19, 23, 24, 69, 74, 76, 86, 87, 89, 92

\newline

lower quartile

=

\_\_

\newline

median

=

\_\_

\newline

upper quartile

=

\_\_

Identify the median: Step $1$ : Identify the median of the data set. $\newline$ Data set: $12, 19, 23, 24, 69, 74, 76, 86, 87, 89, 92$ . $\newline$ Since there are $11$ numbers, the median is the $6$ th number. $\newline$ Calculation: Median $= 74$
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. $\newline$ Data for lower quartile: $12$ , $19$ , $23$ , $24$ , $69$ . $\newline$ Since there are $5$ numbers, the lower quartile is the $3$ rd number. $\newline$ Calculation: Lower quartile $= 23$
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. $\newline$ Data for upper quartile: $76$ , $86$ , $87$ , $89$ , $92$ . $\newline$ Since there are $5$ numbers, the upper quartile is the $3$ rd number. $\newline$ Calculation: Upper quartile $= 87$

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