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Objective: Learn to find measures of variability. Course 3 4-4 Variability.

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Presentation on theme: "Objective: Learn to find measures of variability. Course 3 4-4 Variability."— Presentation transcript:

1 Objective: Learn to find measures of variability. Course Variability

2 Does the mean, median or mode give any indication of how the data is spread out or is it a central view of the data?

3 5 Pieces of Data in Box & Whisker Plot (in order from left to right) 1.Lower extremelowest number 2.First quartilemiddle of lower-half 3.Medianmiddle number 4.Third quartilemiddle of upper half 5.Upper extremelargest number

4 First quartile Third quartile Median Box and Whisker Plot Lower extreme Upper extreme

5 Range--largest minus the smallest; its the entire length of the line

6 Course Variability Litter Size23456 Number of Litters The range of a data set is the largest value minus the smallest value. For the kitten data, the range is 6 2 = 4. Quartiles divide a data set into four equal parts. Heres how to find the 1 st and 3 rd quartiles: 1 st : order data least to greatest 2 nd : if odd amount, middle number is median If even amount, add 2 middle numbers and divide by 2 for median 3 rd : Divide data in half with a line; if odddont include median (draw line through it) if evendraw line between 2 middle data points 4 th : the first quartile is the middle half of the left side of data 5 th : the third quartile is the middle half of the right side of the data Data Lower halfUpper half First quartile: 3 median of lower half Third quartile: 5 median of upper half Median: 4 (second quartile)

7 Find the range and the first and third quartiles for the data set. Additional Example 1A: Finding Measures of Variability Course Variability A. 15, 83, 75, 12, 19, 74, Order the values. range: 83 – 12 = 71 first quartile: 15 third quartile: 75

8 Find the range and the first and third quartiles for the data set. Additional Example 1B: Finding Measures of Variability Course Variability B. 75, 61, 88, 79, 79, 99, 63, 77

9 Find the range and the first and third quartiles for the data set. Try This: Example 1A Course Variability A. 25, 38, 66, 19, 91, 47, 13

10 Course Variability B. 45, 31, 59, 49, 49, 69, 33, 47 Find the range and the first and third quartiles for the data set. Try This: Example 1B

11 Course Variability A box-and-whisker plot shows the distribution of data. The middle half of the data is represented by a box with a vertical line at the median. The lower fourth and upper fourth quarters are represented by whiskers that extend to the smallest and largest values. First quartile Third quartile Median

12 Use the given data to make a box-and-whisker plot: 21, 25, 15, 13, 17, 19, 19, 21 Additional Example 2: Making a Box-and-Whisker Plot Course Variability Step 1. Order the data and find the smallest value, first quartile, median, third quartile, and largest value smallest value: 13 largest value: 25 first quartile: = third quartile: = median: =

13 Step 1. Order the data and find the smallest value, first quartile, median, third quartile, and largest value. Use the given data to make a box-and-whisker plot. Course Variability Step 2. Draw a number line and plot a point above each value from Step 1. smallest value first quartile 16 median 19 third quartile 21 largest value 25 Additional Example 2 Continued

14 Step 2. Draw a number line and plot a point above each value. Use the given data to make a box-and-whisker plot. Course Variability Step 3. Draw the box and whiskers. The left whisker is from the 1 st to 2 nd dot. The right whisker connects the 4 th and 5 th dot. The box connects the 2 nd dot and 4 th dot. Draw a line through the median

15 Use the given data to make a box-and-whisker plot. 31, 23, 33, 35, 26, 24, 31, 29 Try This: Example 2 Course Variability Step 1. Order the data and find the smallest value, first quartile, median, third quartile, and largest value.

16 Use the given data to make a box-and-whisker plot. Course Variability Step 2. Draw a number line and plot a point above each value. Try This: Example 2 Continued

17 Step 2. Draw a number line and plot a point above each value. Use the given data to make a box-and-whisker plot. Course Variability Step 3. Draw the box and whiskers. Try This: Example 2 Continued

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21 Additional Example 3: Comparing Data Sets Using Box-and-Whisker Plots Course Variability These box-and-whisker plots compare the ages of the first ten U.S. presidents with the ages of the last ten presidents (through George W. Bush) when they took office. Note: 57 is the first quartile and the median.

22 Additional Example 3 Continued Course Variability A. Compare the medians and ranges. The median for the first ten presidents is slightly greater. The range for the last ten presidents is greater. Note: 57 is the first quartile and the median.

23 Additional Example 3 Continued Course Variability B. Compare the differences between the third quartile and first quartile for each. Note: 57 is the first quartile and the median.

24 Try This: Example 3 Course Variability Final 1234T Oakland Tampa Bay These box-and- whisker plots compare the scores per quarter at Super Bowl XXXVII. The data in the T column is left out because it is a total of all the quarters. Oakland Tampa Bay

25 Course Variability A. Compare the medians and ranges. Try This: Example 3 Continued Oakland Tampa Bay

26 Course Variability B. Compare the differences between the third quartile and first quartile for each. Try This: Example 3 Continued Oakland Tampa Bay

27 Lesson Quiz: Part 1 Find the range and the first and third quartile for each data set , 52, 68, 32, 53, 47, , 18, 11, 2, 7, 5, 9, 6, 13, 1, 17, 8, 0 Insert Lesson Title Here Course Variability

28 Lesson Quiz: Part 2 Use the following data for problems 3 and 4. 91, 87, 98, 93, 89, 78, Make a box-and-whisker plot 4. What is the mean? Insert Lesson Title Here Course Variability


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