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In the data set below, what are the lower quartile, the median, and the upper quartile? $\newline$ $1, 1, 1, 2, 4, 5, 6, 7, 7, 9, 9$ $\newline$ 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

1, 1, 1, 2, 4, 5, 6, 7, 7, 9, 9

\newline

lower quartile

=

_____

\newline

median

=

_____

\newline

upper quartile

=

_____

Identify the median: Step $1$ : Identify the median of the data set $1, 1, 1, 2, 4, 5, 6, 7, 7, 9, 9$ . Since there are $11$ numbers, the median is the $6$ th number in the sorted list. Calculation: Median $= 5$
Determine lower quartile: Step $2$ : Determine the lower quartile. $\newline$ The lower quartile is the median of the first half of the data set (excluding the median of the entire set if the number of data points is odd). $\newline$ First half: $1, 1, 1, 2, 4$ $\newline$ Calculation: Lower quartile = $1$ (middle value of the first half)
Determine upper quartile: Step $3$ : Determine the upper quartile. $\newline$ The upper quartile is the median of the second half of the data set (excluding the median of the entire set if the number of data points is odd). $\newline$ Second half: $6, 7, 7, 9, 9$ $\newline$ Calculation: Upper quartile $= 7$ (middle value of the second half)

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