Measure of Center And Boxplot’s

Three Measures of Center Mean- average of your values To find- add all values up and divide by how many you Have Median- middle number to find- arrange from least to greatest 3. Mode- most repeated number to find- look for number most often listed

When to use which measure of center… Use mean  when you DO NOT have an outlier Use median  when you DO have an outlier

Example 1 Data Set I Data Set II Mean is ____ Median is ____ Mode is ____ Data Set II Data Set II

Solution Data Set I Data Set II Mean is 483.8461538 Median is 400 Mode is 300 Data Set II Mean is 474 Median is 350 Data Set II

Yesterday we talked displaying data using a histogram, another way to display data is through a box plot. To construct a box plot you need your “5 Number Summary”

5 Number Summary Minimum- smallest value Quartile 1 (Q1) – median of lower half of data Median- middle value Quartile 3 (Q3) – median of upper half of data Maximum – largest value

Where does everything go?.... Min Q1 Median Q3 Max Lower Upper Quartile Quartile “median of lower half” “median of upper half” 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.

IQR Q3 – Q1 = IQR

Example 1 Create a box plot of the data below 59, 27, 18, 78, 61, 91, 52, 34, 54, 93, 100, 87, 85, 82, 68

Luckily…. Our calculator will tell you your 5 number summary Step 1: Enter the height data in L1. Commands: STAT  EDIT (Use 2nd QUIT to exit) Step 2: Find your “best friend” in this unit Commands: STAT  CALC  1: 1-Var Stats  Enter

Example 2: Use the following data set to create a five-number summary and graph the box-and-whisker plot 87, 7, 41, 50, 15, 220, 23, 99, 11, 45, 11, 61, 3, 39, 21

Solution Minimum – 3 Maximum – 220 Median – 39 Q1 – 11 Q3 – 61

You try! Find the mean, median, and mode Create a box plot of the data 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 Find the mean, median, and mode Create a box plot of the data 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