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In the data set below, what are the lower quartile, the median, and the upper quartile? $\newline$ $10, 36, 56, 58, 61, 78, 81, 83, 84, 89, 97$ $\newline$ 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

10, 36, 56, 58, 61, 78, 81, 83, 84, 89, 97

\newline

lower quartile

=

\_\_

\newline

median

=

\_\_

\newline

upper quartile

=

\_\_

Identify the median: Step $1$ : Identify the median of the data set. $\newline$ Data set: $10, 36, 56, 58, 61, 78, 81, 83, 84, 89, 97$ . $\newline$ There are $11$ numbers, so the median is the $6$ th number. $\newline$ Median = $78$
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: $10, 36, 56, 58, 61$ . $\newline$ The lower quartile is the median of these numbers, which is the $3^{\text{rd}}$ number. $\newline$ Lower quartile $= 56$
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: $81, 83, 84, 89, 97$ . $\newline$ The upper quartile is the median of these numbers, which is the $3$ rd number. $\newline$ Upper quartile $= 84$

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