In the data set below, what are the lower quartile, the median, and the upper quartile? 1, 4, 5, 5, 6, 6, 6, 7, 8, 8, 8 lower quartile = _____ median = _____ upper quartile = _____

Arrange and Count Data: Arrange the data set in ascending order and count the number of data points. Data set: 1, 4, 5, 5, 6, 6, 6, 7, 8, 8, 8 Number of data points: 11Calculate Median Position: Calculate the position of the median (which is also the second quartile Q2). Since there are 11 data points, the median is the 6th value when the data is ordered. Median (Q2) = 6Identify Lower Quartile Data: Identify the data set for the lower quartile (Q1). For the lower quartile, consider the first half of the data set, excluding the median. First half: 1, 4, 5, 5, 6 (5 data points)Calculate Lower Quartile Position: Calculate the position of the lower quartile. Since there are 5 data points in the first half, the lower quartile is the average of the 2nd and 3rd values. Lower quartile (Q1) = (4 + 5) / 2 = 4.5Identify Upper Quartile Data: Identify the data set for the upper quartile (Q3). For the upper quartile, consider the second half of the data set, excluding the median. Second half: 6, 7, 8, 8, 8 (5 data points)Calculate Upper Quartile Position: Calculate the position of the upper quartile. Since there are 5 data points in the second half, the upper quartile is the average of the 2nd and 3rd values. Upper quartile (Q3) = (7 + 8) / 2 = 7.5

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In the data set below, what are the lower quartile, the median, and the upper quartile? $\newline$ $1, 4, 5, 5, 6, 6, 6, 7, 8, 8, 8$ $\newline$ 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

1, 4, 5, 5, 6, 6, 6, 7, 8, 8, 8

\newline

lower quartile

=

\_\_

\newline

median

=

\_\_

\newline

upper quartile

=

\_\_

Arrange and Count Data: Arrange the data set in ascending order and count the number of data points. $\newline$ Data set: $1, 4, 5, 5, 6, 6, 6, 7, 8, 8, 8$ $\newline$ Number of data points: $11$
Calculate Median Position: Calculate the position of the median (which is also the second quartile $Q_2$ ). $\newline$ Since there are $11$ data points, the median is the $6$ th value when the data is ordered. $\newline$ Median ( $Q_2$ ) = $6$
Identify Lower Quartile Data: Identify the data set for the lower quartile ( $Q_1$ ). $\newline$ For the lower quartile, consider the first half of the data set, excluding the median. $\newline$ First half: $1, 4, 5, 5, 6$ ( $5$ data points)
Calculate Lower Quartile Position: Calculate the position of the lower quartile. Since there are $5$ data points in the first half, the lower quartile is the average of the $2$ nd and $3$ rd values. Lower quartile $(Q_1) = \frac{(4 + 5)}{2} = 4.5$
Identify Upper Quartile Data: Identify the data set for the upper quartile ( $Q_3$ ). $\newline$ For the upper quartile, consider the second half of the data set, excluding the median. $\newline$ Second half: $6, 7, 8, 8, 8$ ( $5$ data points)
Calculate Upper Quartile Position: Calculate the position of the upper quartile. $\newline$ Since there are $5$ data points in the second half, the upper quartile is the average of the $2$ nd and $3$ rd values. $\newline$ Upper quartile $(Q_3) = \frac{(7 + 8)}{2} = 7.5$