Quiz

Boxplots Min Q1 Median Q3 Max Lower Upper Quartile Quartile Discuss how to draw a box plot by hand. First, you must know the “five-number summary” of the data. Use the max and min to determine an appropriate scale to use. Minimum (min) Lower Quartile (Q1) Median (M) Upper Quartile (Q3) Maximum (max)   We use these 5 numbers to construct the boxplot. The quartiles form the edges of the “box,” the median is a line inside the box, and the max and min are attached to the sides of the box with “whiskers.” Thus this graph is sometimes called a box-and-whisker plot. Discuss how to find shape, center and spread from the boxplot. For example: The shape of our buttons distribution is skewed right since the right whisker is a lot longer than the left whisker. The center is the line in the middle of the box that corresponds to the median. For the spread we can easily see how far out each whisker reaches (the range). We can also look at the length of the box. To find the length, we can subtract Q3 – Q1. This difference is known as the interquartile range (IQR for short), because it measures how spread out the quartiles are.

Five Number Summary A five number summary is five numbers that describe a data distribution. Minimum, Q1, Median, Q3, Maximum Minimum: 3 Maximum: 24 Median: (11+13)/2 = 12 Q1 and Q3 are the medians of the lower and upper halves.

Box and Whisker Plot 3 24 10 12 19

Practice! Below is a stem and leaf plot of the amount of money spent by 25 shoppers at a grocery store. Stem Leaf 1 2 3 4 5 6 7 8 9 10 11 3 6 0 1 7 8 9 0 0 3 6 8 1 3 4 7 2 5 5 0 5 2 6 Guided practice: Ask if students know how to read a stem and leaf plot. Have a student explain to the rest of the class how to read the plot. Key: 42 = $42

Practice! Calculate the mean and median. Stem Leaf 1 2 3 4 5 6 7 8 9 10 11 3 6 0 1 7 8 9 0 0 3 6 8 1 3 4 7 2 5 5 0 5 2 6 Calculate the mean and median. Calculate the lower and upper quartiles and IQR. Determine which, if any, values are outliers. Write several sentences to describe this data set in context. Name some factors that might account for the extreme values, and the much lower measure of center. median $31, mean lower quartile $18.50, upper quartile $47.50, IQR 29   LQ – 1.5 (IQR) = -25 No outliers UQ +1.5(IQR) = 91 97 & 113 are outliers Ex – note low center, big spread, two extreme values, on upper end of data Ex – extreme values – larger family, shopping for entire week Lower values – quick tips Key: 42 = $42