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

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?

5 Pieces of Data in Box & Whisker Plot (in order from left to right) Lower extreme—lowest number First quartile—middle of lower-half Median—middle number Third quartile—middle of upper half Upper extreme—largest number

Box and Whisker Plot Upper extreme Lower extreme 1 2 3 4 5 6 7 8 9 Median First quartile Third quartile

Range--largest minus the smallest; it’s the entire length of the line 1 2 3 4 5 6 7 8 9 Range--largest minus the smallest; it’s the entire length of the line

Course 3 4-4 Variability Data The range of a data set is the largest value minus the smallest value. For the kitten data, the range is 6 — 2 = 4. Lower half Upper half 2 3 3 3 3 3 3 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 6 First quartile: 3 median of lower half Median: 4 (second quartile) Third quartile: 5 median of upper half Litter Size 2 3 4 5 6 Number of Litters 1 8 11 Quartiles divide a data set into four equal parts. Here’s how to find the 1st and 3rd quartiles: 1st: order data least to greatest 2nd: if odd amount, middle number is median If even amount, add 2 middle numbers and divide by 2 for median 3rd: Divide data in half with a line; if odd—don’t include median (draw line through it) if even—draw line between 2 middle data points 4th: the first quartile is the middle half of the left side of data 5th: the third quartile is the middle half of the right side of the data

Additional Example 1A: Finding Measures of Variability Course 3 4-4 Variability Additional Example 1A: Finding Measures of Variability Find the range and the first and third quartiles for the data set. A. 15, 83, 75, 12, 19, 74, 21 12 15 19 21 74 75 83 Order the values. range: 83 – 12 = 71 first quartile: 15 third quartile: 75

Additional Example 1B: Finding Measures of Variability Course 3 4-4 Variability Additional Example 1B: Finding Measures of Variability Find the range and the first and third quartiles for the data set. B. 75, 61, 88, 79, 79, 99, 63, 77

4-4 Variability Try This: Example 1A Course 3 4-4 Variability Try This: Example 1A Find the range and the first and third quartiles for the data set. A. 25, 38, 66, 19, 91, 47, 13

4-4 Variability Try This: Example 1B Course 3 4-4 Variability Try This: Example 1B Find the range and the first and third quartiles for the data set. B. 45, 31, 59, 49, 49, 69, 33, 47

Course 3 4-4 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. 1 2 3 4 5 6 7 8 9 Median First quartile Third quartile

Use the given data to make a box-and-whisker plot: Course 3 4-4 Variability Additional Example 2: Making a Box-and-Whisker Plot Use the given data to make a box-and-whisker plot: 21, 25, 15, 13, 17, 19, 19, 21 Step 1. Order the data and find the smallest value, first quartile, median, third quartile, and largest value. 13 15 17 19 19 21 21 25 smallest value: 13 largest value: 25 first quartile: = 16 15 + 17 2 third quartile: = 21 21 + 21 2 median: = 19 19 + 19 2

Use the given data to make a box-and-whisker plot. Course 3 4-4 Variability Additional Example 2 Continued Use the given data to make a box-and-whisker plot. Step 1. Order the data and find the smallest value, first quartile, median, third quartile, and largest value. Step 2. Draw a number line and plot a point above each value from Step 1. 13 15 17 19 19 21 21 25 smallest value 13 first quartile 16 median 19 third quartile 21 largest value 25 12 14 16 18 20 22 24 26 28

Use the given data to make a box-and-whisker plot. Course 3 4-4 Variability Use the given data to make a box-and-whisker plot. Step 3. Draw the box and whiskers. The left whisker is from the 1st to 2nd dot. The right whisker connects the 4th and 5th dot. The box connects the 2nd dot and 4th dot. Draw a line through the median. Step 2. Draw a number line and plot a point above each value. 13 15 17 19 19 21 21 25 12 14 16 18 20 22 24 26 28

Use the given data to make a box-and-whisker plot. Course 3 4-4 Variability Try This: Example 2 Use the given data to make a box-and-whisker plot. 31, 23, 33, 35, 26, 24, 31, 29 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 3 4-4 Variability Try This: Example 2 Continued Use the given data to make a box-and-whisker plot. Step 2. Draw a number line and plot a point above each value. 22 24 26 28 30 32 34 36 38

Use the given data to make a box-and-whisker plot. Course 3 4-4 Variability Try This: Example 2 Continued Use the given data to make a box-and-whisker plot. Step 3. Draw the box and whiskers. Step 2. Draw a number line and plot a point above each value. 22 24 26 28 30 32 34 36 38

Additional Example 3: Comparing Data Sets Using Box-and-Whisker Plots Course 3 4-4 Variability Additional Example 3: Comparing Data Sets Using Box-and-Whisker Plots Note: 57 is the first quartile and the median. 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.

Additional Example 3 Continued Course 3 4-4 Variability Additional Example 3 Continued Note: 57 is the first quartile and the median. 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.

Additional Example 3 Continued Course 3 4-4 Variability Additional Example 3 Continued Note: 57 is the first quartile and the median. B. Compare the differences between the third quartile and first quartile for each.

4-4 Variability Try This: Example 3 Oakland Course 3 4-4 Variability Try This: Example 3 Final 1 2 3 4 T Oakland 6 12 21 Tampa Bay 17 14 48 Oakland 0 3 6 9 12 15 18 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.

Try This: Example 3 Continued Course 3 4-4 Variability Try This: Example 3 Continued A. Compare the medians and ranges. Oakland 0 3 6 9 12 15 18 Tampa Bay

Try This: Example 3 Continued Course 3 4-4 Variability Try This: Example 3 Continued B. Compare the differences between the third quartile and first quartile for each. Oakland 0 3 6 9 12 15 18 Tampa Bay

Insert Lesson Title Here Course 3 4-4 Variability Insert Lesson Title Here Lesson Quiz: Part 1 Find the range and the first and third quartile for each data set. 1. 48, 52, 68, 32, 53, 47, 51 2. 3, 18, 11, 2, 7, 5, 9, 6, 13, 1, 17, 8, 0

Insert Lesson Title Here Course 3 4-4 Variability Insert Lesson Title Here Lesson Quiz: Part 2 Use the following data for problems 3 and 4. 91, 87, 98, 93, 89, 78, 94 3. Make a box-and-whisker plot 4. What is the mean?