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In the data set below, what are the lower quartile, the median, and the upper quartile? $\newline$ $2, 2, 2, 3, 5, 5, 7, 7$ $\newline$ 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

2, 2, 2, 3, 5, 5, 7, 7

\newline

lower quartile

=

\_\_

\newline

median

=

\_\_

\newline

upper quartile

=

\_\_

Calculate Median: Step $1$ : Identify the median of the data set $2, 2, 2, 3, 5, 5, 7, 7$ . Since there are $8$ numbers, the median will be the average of the $4$ th and $5$ th numbers. Calculation: $(3 + 5) / 2 = 4$
Lower Quartile Data Set: Step $2$ : Identify the data set for the lower quartile. $\newline$ Consider the first half of the data set, excluding the median. $\newline$ First half: $2, 2, 2, 3$ $\newline$ Calculation: Median of $2, 2, 2, 3$ is the average of the $2$ nd and $3$ rd numbers, $(2 + 2) / 2 = 2$
Upper Quartile Data Set: Step $3$ : Identify the data set for the upper quartile. $\newline$ Consider the second half of the data set, excluding the median. $\newline$ Second half: $5, 5, 7, 7$ $\newline$ Calculation: Median of $5, 5, 7, 7$ is the average of the $2$ nd and $3$ rd numbers, $(5 + 7) / 2 = 6$

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