In the data set below, what are the lower quartile, the median, and the upper quartile? $\newline$ $3, 4, 4, 6, 6, 8, 8, 8, 9, 9$ $\newline$ lower quartile $=$ $\_\_$ $\newline$ median $=$ $\_\_$ $\newline$ upper quartile $=$ $\_\_$

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Algebra 1

Calculate quartiles and interquartile range

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Q. In the data set below, what are the lower quartile, the median, and the upper quartile?

\newline

3, 4, 4, 6, 6, 8, 8, 8, 9, 9

\newline

lower quartile

=

\_\_

\newline

median

=

\_\_

\newline

upper quartile

=

\_\_

Arrange and Find Median: Arrange the data set in ascending order and find the median. $\newline$ The data set is already in ascending order: $3, 4, 4, 6, 6, 8, 8, 8, 9, 9$ . $\newline$ Since there are $10$ numbers, the median will be the average of the $5$ th and $6$ th numbers. $\newline$ Median: $(6 + 6) / 2 = 12 / 2 = 6$ .
Identify Lower Quartile Data: Identify the data set for the lower quartile. $\newline$ For the lower quartile, consider the first half of the data set, excluding the median if necessary. $\newline$ First half is $3, 4, 4, 6, 6$ . $\newline$ Lower quartile data: $3, 4, 4, 6, 6$ .
Find Lower Quartile Value: Find the value of the lower quartile. $\newline$ Lower quartile data: $3, 4, 4, 6, 6$ . $\newline$ For an odd number of observations, the median is the middle number. $\newline$ Lower quartile is the median of the first half, which is the $3$ rd number: $4$ .
Identify Upper Quartile Data: Identify the data set for the upper quartile. $\newline$ For the upper quartile, consider the second half of the data set, excluding the median if necessary. $\newline$ Second half is $8, 8, 8, 9, 9$ . $\newline$ Upper quartile data: $8, 8, 8, 9, 9$ .
Find Upper Quartile Value: Find the value of the upper quartile. $\newline$ Upper quartile data: $8, 8, 8, 9, 9$ . $\newline$ For an odd number of observations, the median is the middle number. $\newline$ Upper quartile is the median of the second half, which is the $3$ rd number: $8$ .
Write Quartile Values: Write the values of the lower quartile, median, and the upper quartile. $\newline$ Lower quartile = $4$ $\newline$ Median = $6$ $\newline$ Upper quartile = $8$