Box-and-Whisker Plots We have learned various ways of organizing data so far. We have learned –Line graphs –Bar Graphs –Tables Next we will learn Box-and-Whisker Plots.

Box-and-Whisker Plots Vocabulary –Box-and-Whisker Plot –Upper Quartile (UQ) –Lower Quartile (LQ) –Median –Upper Extreme –Lower Extreme –Interquartile range

Box-and-Whisker Plots So what is a box and whisker plot? A visual way to see the biggest number, lowest number, median of the set, median of the upper half of a set, and the median of the lower half of a set. We will use a Box and lines extending from the box (whiskers) to show these values.

Box-and-Whisker Plots To make a box-and-whisker plot, I need 5 things. (Before finding these, always put the data in order first.) 1.Upper Extreme (UE) 2.Lower extreme (LE) 3.Median 4.Upper Quartile (UQ) 5.Lower Quartile (LQ)

Five Values needed to make a Box-and-Whisker Plot 1. Upper Extreme- the largest value in a set of data. 2. Lower Extreme – the smallest value in a set of data. Ex. In the set 1,2,3,4,5,6,7; what is the upper extreme and the lower extreme? Upper Extreme: 7 Lower Extreme: 1

Five Values needed to make a Box-and-Whisker Plot 3. Median – Middle number when the values are written from least to greatest. 4. Upper Quartile (UQ) – When the values of a set are split into two groups by the median, the median of the upper half is called the upper quartile.

Example of Median The median of this set of numbers is the number in the middle when the numbers are written in order. 1,2,3,4,5,6,7 So what is the median of: 1,2,3,4,5,6,7 So 4 is the median for our data set.

Example of Upper Quartile Ex. Set of data: 1,2,3,4,5,6,7 The numbers are written from least to greatest. The middle value is 4, so 4 is the median. So 4 splits the numbers in half. So now I cover up the median and look at all values to the RIGHT (the upper half). 1,2,3,4,5,6,7 The median of the values to the right of the median is called the upper quartile (UQ). So what is the median of 5,6,7? 6 So 6 is the upper quartile (UQ) for our data set.

Five Values needed to make a Box-and-Whisker Plot 5. Lower Quartile (LQ)- When the values of a set are split into two groups by the median, the median of the lower half is called the lower quartile.

Example of Lower Quartile (LQ) Ex. Set of data: 1,2,3,4,5,6,7 The numbers are written from least to greatest. The middle value is 4, so 4 is the median. So 4 splits the numbers in half. So now I cover up the median and look at all values to the LEFT (the lower half). 1,2,3,4,5,6,7 The median of the values to the right of the median is called the upper quartile (UQ). So what is the median of 1,2,3? 2 So 2 is the Lower Quartile (LQ) for our data set.

Five Values needed to make a Box-and-Whisker Plot So now we have all five necessary items for our data set: 1,2,3,4,5,6,7 1.Upper Extreme = 7 2.Lower extreme = 1 3.Median = 4 4.Upper Quartile (UQ) = 6 5.Lower Quartile (LQ) = 2

Box-and-Whisker Plot

Interquartile Range Interquartile Range – subtract the lower quartile (left side of the box) from the upper quartile (right side of the box). [UQ (right side of box )] – [LQ (left side of the box )] Example for our data UQ = 6 LQ = 2 Interquartile range = UQ – LQ = 6 – 2 = 4

Box-and-Whisker Plot (Practice #1) UE = LE = Median = UQ = LQ = 2, 4, 6, 8, 10, 12, 14, Create the box-and-whisker plot on your sheet.

Box-and-Whisker Plot (Practice #2) UE = LE = Median = UQ = LQ = 12, 15, 24, 31, 38, 39, 42, 50, Create the box-and-whisker plot on your sheet.