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In the data set below, what are the lower quartile, the median, and the upper quartile? $\newline$ $1, 1, 2, 2, 4, 5, 5, 5, 6, 7, 7$ $\newline$ 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, 2, 2, 4, 5, 5, 5, 6, 7, 7

\newline

lower quartile

=

\_\_

\newline

median

=

\_\_

\newline

upper quartile

=

\_\_

Identify Median: Step $1$ : Identify the median of the data set $1, 1, 2, 2, 4, 5, 5, 5, 6, 7, 7$ . Since there are $11$ data points, the median is the $6$ th value when arranged in ascending order. Calculation: The $6$ th value is $5$ .
Lower Quartile Data: Step $2$ : Identify the data set for the lower quartile. $\newline$ For the lower quartile, consider the first half of the data set, excluding the median. $\newline$ First half is $1, 1, 2, 2, 4$ . $\newline$ Calculation: The median of this subset is the $3$ rd value, which is $2$ .
Upper Quartile Data: Step $3$ : Identify the data set for the upper quartile. $\newline$ For the upper quartile, consider the second half of the data set, excluding the median. $\newline$ Second half is $5, 5, 6, 7, 7$ . $\newline$ Calculation: The median of this subset is the $3$ rd value, which is $6$ .

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