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In the data set below, what are the lower quartile, the median, and the upper quartile? $\newline$ $45, 55, 55, 87, 88, 93$ $\newline$ 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

45, 55, 55, 87, 88, 93

\newline

lower quartile = _____

\newline

median = _____

\newline

upper quartile = _____

Calculate Median: Step $1$ : Identify the median of the data set $45, 55, 55, 87, 88, 93$ . Since there are $6$ numbers, the median is the average of the $3$ rd and $4$ th numbers. Calculation: $(55 + 87) / 2 = 142 / 2 = 71$ .
Identify Lower Quartile: Step $2$ : Identify the data set for the lower quartile. $\newline$ Consider the first half of the data set for the lower quartile: $45$ , $55$ , $55$ . $\newline$ Calculation: Median of $45$ , $55$ , $55$ is $55$ (middle value).
Identify Upper Quartile: Step $3$ : Identify the data set for the upper quartile. $\newline$ Consider the second half of the data set for the upper quartile: $87$ , $88$ , $93$ . $\newline$ Calculation: Median of $87$ , $88$ , $93$ is $88$ (middle value).

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