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In the data set below, what are the lower quartile, the median, and the upper quartile? $\newline$ $1, 1, 1, 2, 4, 5, 7, 7$ $\newline$ 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

1, 1, 1, 2, 4, 5, 7, 7

\newline

lower quartile

=

\_\_

\newline

median

=

\_\_

\newline

upper quartile

=

\_\_

Calculate Median: Step $1$ : Identify the median of the data set $1, 1, 1, 2, 4, 5, 7, 7$ . Since there are $8$ numbers, the median will be the average of the $4$ th and $5$ th numbers. Calculation: $(2 + 4) / 2 = 3$ .
Determine Lower Quartile: Step $2$ : Determine the lower quartile. $\newline$ The lower quartile is the median of the first half of the data set. First half: $1, 1, 1, 2$ . $\newline$ Calculation: Since there are $4$ numbers, the lower quartile is the average of the $2$ nd and $3$ rd numbers. $\newline$ $1 + 1 = 2$ , $2 / 2 = 1$ .
Find Upper Quartile: Step $3$ : Determine the upper quartile. $\newline$ The upper quartile is the median of the second half of the data set. Second half: $4, 5, 7, 7$ . $\newline$ Calculation: Since there are $4$ numbers, the upper quartile is the average of the $2$ nd and $3$ rd numbers. $\newline$ $5 + 7 = 12$ , $12 / 2 = 6$ .

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