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In the data set below, what are the lower quartile, the median, and the upper quartile? $\newline$ $3, 4, 4, 4, 5, 7, 7, 7, 8, 9$ $\newline$ 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

3, 4, 4, 4, 5, 7, 7, 7, 8, 9

\newline

lower quartile

=

\_\_\_\_

\newline

median

=

\_\_\_\_

\newline

upper quartile

=

\_\_\_\_

Identify Median: Step $1$ : Identify the median of the data set $3, 4, 4, 4, 5, 7, 7, 7, 8, 9$ . Since there are $10$ data points, the median will be the average of the $5$ th and $6$ th values. $5$ th value = $5$ , $6$ th value = $7$ . Calculation: $(5 + 7) / 2 = 6$ . Median = $6$
Lower Quartile: Step $2$ : Determine the lower quartile. $\newline$ Consider the first half of the data set for the lower quartile: $3, 4, 4, 4, 5$ . $\newline$ Since there are $5$ data points, the lower quartile is the middle value, which is the $3$ rd value. $\newline$ Lower quartile $= 4$
Upper Quartile: Step $3$ : Determine the upper quartile. $\newline$ Consider the second half of the data set for the upper quartile: $7, 7, 7, 8, 9$ . $\newline$ Since there are $5$ data points, the upper quartile is the middle value, which is the $3$ rd value. $\newline$ Upper quartile $= 7$

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