In the data set below, what are the lower quartile, the median, and the upper quartile? 1, 2, 2, 2, 2, 3, 3, 4, 7, 7, 8 lower quartile = _____ median = _____ upper quartile = _____

Arrange Data Set: Arrange the data set in ascending order and count the number of data points. Data set: 1, 2, 2, 2, 2, 3, 3, 4, 7, 7, 8 Number of data points: 11Calculate Median: Calculate the position of the median (which is also the second quartile Q2). Since there are 11 data points, the median is the 6th number in the ordered list. Median (Q2) = 3Identify Lower Quartile: 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, 2, 2, 2, 2Find Lower Quartile: Find the value of the lower quartile (Q1). Since there are 5 numbers in the first half, the lower quartile is the middle number. Lower quartile (Q1) = 2Identify Upper Quartile: 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: 3, 4, 7, 7, 8Find Upper Quartile: Find the value of the upper quartile (Q3). Since there are 5 numbers in the second half, the upper quartile is the middle number. Upper quartile (Q3) = 7

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In the data set below, what are the lower quartile, the median, and the upper quartile? $\newline$ $1, 2, 2, 2, 2, 3, 3, 4, 7, 7, 8$ $\newline$ lower quartile $=$ $\_\_$ $\newline$ median $=$ $\_\_$ $\newline$ upper quartile $=$ $\_\_$

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Math Problems

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, 2, 2, 2, 2, 3, 3, 4, 7, 7, 8

\newline

lower quartile

=

\_\_

\newline

median

=

\_\_

\newline

upper quartile

=

\_\_

Arrange Data Set: Arrange the data set in ascending order and count the number of data points. $\newline$ Data set: $1, 2, 2, 2, 2, 3, 3, 4, 7, 7, 8$ $\newline$ Number of data points: $11$
Calculate Median: 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 $6^{\text{th}}$ number in the ordered list. $\newline$ Median ( $Q_2$ ) = $3$
Identify Lower Quartile: 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: $1, 2, 2, 2, 2$
Find Lower Quartile: Find the value of the lower quartile (Q $1$ ). Since there are $5$ numbers in the first half, the lower quartile is the middle number. Lower quartile $(Q1) = 2$
Identify Upper Quartile: 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: $3, 4, 7, 7, 8$
Find Upper Quartile: Find the value of the upper quartile $Q_3$ . Since there are $5$ numbers in the second half, the upper quartile is the middle number. Upper quartile $Q_3 = 7$