In the data set below, what are the lower quartile, the median, and the upper quartile? 20, 20, 40, 56, 75, 75 lower quartile = _____ median = _____ upper quartile = _____

Arrange Data Set: Arrange the data set in ascending order if it is not already sorted. The given data set is: 20, 20, 40, 56, 75, 75. It is already in ascending order, so no sorting is needed.Find Median: Find the median of the data set. Since there are 6 numbers, the median will be the average of the 3rd and 4th numbers. Median = (40 + 56) / 2 = 96 / 2 = 48.Lower Quartile Data: Identify the data set for the lower quartile. For the lower quartile, consider the first half of the data set, excluding the median if it is not part of the data points. First half is 20, 20, 40. Lower quartile data: 20, 20, 40.Find Lower Quartile: Find the value of the lower quartile. Since there are 3 numbers in the lower half, the lower quartile is the middle number. Lower quartile = 20.Upper Quartile Data: Identify the data set for the upper quartile. For the upper quartile, consider the second half of the data set, excluding the median if it is not part of the data points. Second half is 56, 75, 75. Upper quartile data: 56, 75, 75.Find Upper Quartile: Find the value of the upper quartile. Since there are 3 numbers in the upper half, the upper quartile is the middle number. Upper quartile = 75.

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In the data set below, what are the lower quartile, the median, and the upper quartile? $\newline$ $20, 20, 40, 56, 75, 75$ $\newline$ 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

20, 20, 40, 56, 75, 75

\newline

lower quartile = _____

\newline

median = _____

\newline

upper quartile = _____

Arrange Data Set: Arrange the data set in ascending order if it is not already sorted. $\newline$ The given data set is: $20, 20, 40, 56, 75, 75$ . $\newline$ It is already in ascending order, so no sorting is needed.
Find Median: Find the median of the data set. $\newline$ Since there are $6$ numbers, the median will be the average of the $3$ rd and $4$ th numbers. $\newline$ Median = $(40 + 56) / 2 = 96 / 2 = 48$ .
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 it is not part of the data points. $\newline$ First half is $20$ , $20$ , $40$ . $\newline$ Lower quartile data: $20$ , $20$ , $40$ .
Find Lower Quartile: Find the value of the lower quartile. $\newline$ Since there are $3$ numbers in the lower half, the lower quartile is the middle number. $\newline$ Lower quartile $= 20$ .
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 it is not part of the data points. $\newline$ Second half is $56$ , $75$ , $75$ . $\newline$ Upper quartile data: $56$ , $75$ , $75$ .
Find Upper Quartile: Find the value of the upper quartile. $\newline$ Since there are $3$ numbers in the upper half, the upper quartile is the middle number. $\newline$ Upper quartile $= 75$ .