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In the data set below, what are the lower quartile, the median, and the upper quartile? $\newline$ $10, 11, 16, 16, 40, 48, 59, 59, 68, 92$ $\newline$ 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

10, 11, 16, 16, 40, 48, 59, 59, 68, 92

\newline

lower quartile

=

\_\_

\newline

median

=

\_\_

\newline

upper quartile

=

\_\_

Identify the median: Step $1$ : Identify the median of the data set. $\newline$ Data set: $10, 11, 16, 16, 40, 48, 59, 59, 68, 92$ . $\newline$ Since there are $10$ numbers, the median will be the average of the $5$ th and $6$ th numbers. $\newline$ Calculation: $(40 + 48) / 2 = 44$ .
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: $10, 11, 16, 16, 40$ . $\newline$ The lower quartile is the median of this subset. $\newline$ Calculation: The third number is $16$ .
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: $48, 59, 59, 68, 92$ . $\newline$ The upper quartile is the median of this subset. $\newline$ Calculation: The third number is $59$ .

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