4-4VariabilityCourse 3Warm Up1. Order the test scores from least to greatest: 89, 93, 79, 87, 91, 88, 92.2. Find the median of the test scores.Find the difference.3. 17 – 0.9 4. 8.4 – 7. 616.13.45. 9.1 – 5.7 6. 190.3 – 23.4

4-4VariabilityCourse 3Objective: Learnto 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 numberFirst quartile—middle of lower-halfMedian—middle numberThird quartile—middle of upper halfUpper extreme—largest number

1 2 3 4 5 6 7 8 9Box and Whisker PlotUpper extremeLower extremeMedianFirst quartileThird quartile

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

4-4VariabilityThird quartile: 5 median of upper halfFirst quartile: 3 median of lower halfMedian: 4 (second quartile)Course 3DataThe range of a data set is the largest value minus the smallest value. For the kitten data, the range is 6 — 2 = 4.Lower halfUpper half2 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 6Quartilesdivide a data set into four equal parts. Here’s how to find the 1st and 3rd quartiles:1st: order data least to greatest2nd: if odd amount, middle number is medianIf even amount, add 2 middle numbers and divide by 2 for median3rd: 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 points4th: the first quartile is the middle half of the left side of data5th: the third quartile is the middle half of the right side of the data

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

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

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

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

4-4Variability 1 2 3 4 5 6 7 8 9Course 3A box-and-whiskerplot 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.MedianFirst quartileThird quartile

4-4Variability15 + 17221 + 212third quartile: = 21first quartile: = 16 19 + 192median: = 19Course 3Additional Example 2: Making a Box-and-Whisker PlotUse the given data to make a box-and-whisker plot: 21, 25, 15, 13, 17, 19, 19, 21Step 1. Order the data and find the smallest value, first quartile, median, third quartile, and largest value. 13 15 17 19 19 21 21 25smallest value: 13largest value: 25

4-4Variability12 14 16 18 20 22 24 26 28Course 3Additional Example 2 ContinuedUse the given data to make a box-and-whisker plot.Step 2. Draw a number line and plot a point above each value from Step 1. 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 25smallest value 13first quartile 16third quartile 21largest value 25median 19

4-4Variability12 14 16 18 20 22 24 26 28Course 3Use 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

4-4VariabilityCourse 3Try This: Example 2Use the given data to make a box-and-whisker plot. 31, 23, 33, 35, 26, 24, 31, 29Step 1. Order the data and find the smallest value, first quartile, median, third quartile, and largest value.

4-4Variability22 24 26 28 30 32 34 36 38Course 3Try This: Example 2 ContinuedUse the given data to make a box-and-whisker plot.Step 2. Draw a number line and plot a point above each value.

4-4Variability22 24 26 28 30 32 34 36 38Course 3Try This: Example 2 ContinuedUse 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.

4-4VariabilityCourse 3Additional Example 3: Comparing Data Sets Using Box-and-Whisker PlotsNote: 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.

4-4VariabilityCourse 3Additional Example 3 ContinuedNote: 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.

4-4VariabilityCourse 3Additional Example 3 ContinuedNote: 57 is the first quartile and the median.B. Compare the differences between the third quartile and first quartile for each.

4-4VariabilityOakland0 3 6 9 12 15 18Tampa Bay0 3 6 9 12 15 18Course 3Try This: Example 3These 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.

4-4VariabilityOakland0 3 6 9 12 15 18Tampa Bay0 3 6 9 12 15 18Course 3Try This: Example 3 ContinuedA. Compare the medians and ranges.

4-4VariabilityOakland0 3 6 9 12 15 18Tampa Bay0 3 6 9 12 15 18Course 3Try This: Example 3 ContinuedB. Compare the differences between the third quartile and first quartile for each.

4-4VariabilityCourse 3Insert Lesson Title HereLesson Quiz: Part 1Find the range and the first and third quartile for each data set. 1. 48, 52, 68, 32, 53, 47, 512. 3, 18, 11, 2, 7, 5, 9, 6, 13, 1, 17, 8, 0

4-4VariabilityCourse 3Insert Lesson Title HereLesson Quiz: Part 2Use the following data for problems 3 and 4. 91, 87, 98, 93, 89, 78, 943. Make a box-and-whisker plot4. What is the mean?