objective: learn to find measures of variability. course 3 4-4 variability
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Objective: Learn to find measures of variability.
Course 3
4-4 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)
1.Lower extreme—lowest number
2.First quartile—middle of lower-half
3.Median—middle number
4.Third quartile—middle of upper half
5.Upper extreme—largest number
1 2 3 4 5 6 7 8 9
First quartile Third quartileMedian
Box and Whisker Plot
Lower extremeUpper extreme
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
Litter Size 2 3 4 5 6
Number of Litters
1 6 8 11 1
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. 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
Data
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 6Lower half Upper half
First quartile: 3 median of lower half
Third quartile: 5 median of upper half
Median: 4 (second quartile)
Find the range and the first and third quartiles for the data set.
Additional Example 1A: Finding Measures of Variability
Course 3
4-4 Variability
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
Find the range and the first and third quartiles for the data set.
Additional Example 1B: Finding Measures of Variability
Course 3
4-4 Variability
B. 75, 61, 88, 79, 79, 99, 63, 77
Find the range and the first and third quartiles for the data set.
Try This: Example 1A
Course 3
4-4 Variability
A. 25, 38, 66, 19, 91, 47, 13
Course 3
4-4 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
Course 3
4-4 Variability
1 2 3 4 5 6 7 8 9
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 quartileMedian
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 3
4-4 Variability
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
2third quartile: = 21
21 + 21
2
median: = 1919 + 19
2
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
12 14 16 18 20 22 24 26 28
Step 2. Draw a number line and plot a point above each value from Step 1.
smallest value
13
13 15 17 19 19 21 21 25first
quartile 16
median
19
third quartile
21
largest value
25
Additional Example 2 Continued
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 3
4-4 Variability
12 14 16 18 20 22 24 26 28
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.
13 15 17 19 19 21 21 25
Use the given data to make a box-and-whisker plot.
31, 23, 33, 35, 26, 24, 31, 29
Try This: Example 2
Course 3
4-4 Variability
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
22 24 26 28 30 32 34 36 38
Step 2. Draw a number line and plot a point above each value.
Try This: Example 2 Continued
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 3
4-4 Variability
22 24 26 28 30 32 34 36 38
Step 3. Draw the box and whiskers.
Try This: Example 2 Continued
Additional Example 3: Comparing Data Sets Using Box-and-Whisker Plots
Course 3
4-4 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.
Additional Example 3 Continued
Course 3
4-4 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.
Additional Example 3 Continued
Course 3
4-4 Variability
B. Compare the differences between the third quartile and first quartile for each.
Note: 57 is the first quartile and the median.
Try This: Example 3
Course 3
4-4 Variability
Final 1 2 3 4 T
Oakland 3 0 6 12 21
Tampa Bay 3 17 14 14 48
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
0 3 6 9 12 15 18
Tampa Bay
0 3 6 9 12 15 18
Course 3
4-4 Variability
A. Compare the medians and ranges.
Try This: Example 3 Continued
Oakland
0 3 6 9 12 15 18
Tampa Bay
0 3 6 9 12 15 18
Course 3
4-4 Variability
B. Compare the differences between the third quartile and first quartile for each.
Try This: Example 3 Continued
Oakland
0 3 6 9 12 15 18
Tampa Bay
0 3 6 9 12 15 18
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
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Course 3
4-4 Variability
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?
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Course 3
4-4 Variability