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

\newline

lower quartile

=

\_\_

\newline

median

=

\_\_

\newline

upper quartile

=

\_\_

Identify Median Calculation: Step $1$ : Identify the median of the data set $1, 1, 2, 2, 2, 4, 4, 6, 6, 7$ . Since there are $10$ data points, the median will be the average of the $5$ th and $6$ th values. Calculation: $(2 + 4) / 2 = 3$
Lower Quartile Determination: Step $2$ : Determine the lower quartile, which is the median of the first half of the data set. $\newline$ First half: $1, 1, 2, 2, 2$ $\newline$ The lower quartile is the middle value of the first half. $\newline$ Calculation: Middle value is $2$
Upper Quartile Calculation: Step $3$ : Determine the upper quartile, which is the median of the second half of the data set. $\newline$ Second half: $4, 4, 6, 6, 7$ $\newline$ The upper quartile is the middle value of the second half. $\newline$ Calculation: Middle value is $6$

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