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In the data set below, what are the lower quartile, the median, and the upper quartile? $\newline$ $18, 20, 21, 56, 63, 73, 86$ $\newline$ lower quartile $=$ $\_\_\_\_$ $\newline$ median $=$ $\_\_\_\_$ $\newline$ upper quartile $=$ $\_\_\_\_$

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Calculate quartiles and interquartile range

Full solution

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

\newline

18, 20, 21, 56, 63, 73, 86

\newline

lower quartile

=

\_\_\_\_

\newline

median

=

\_\_\_\_

\newline

upper quartile

=

\_\_\_\_

Identify the median: Step $1$ : Identify the median of the data set $18, 20, 21, 56, 63, 73, 86$ . Since there are $7$ numbers, the median is the fourth number. Calculation: Median $= 56$
Determine lower quartile: Step $2$ : Determine the lower quartile. $\newline$ The lower quartile is the median of the first half of the data set (excluding the median of the entire set). $\newline$ First half: $18$ , $20$ , $21$ . $\newline$ Calculation: Lower quartile $= 20$
Determine upper quartile: Step $3$ : Determine the upper quartile. $\newline$ The upper quartile is the median of the second half of the data set (excluding the median of the entire set). $\newline$ Second half: $63, 73, 86$ . $\newline$ Calculation: Upper quartile $= 73$

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