### Lesson 12-2

```Lesson 13-3
Range – the difference between the greatest and least data
Example 1 Find Range
Find the range for each set of data.
a. The length in days of family vacations: 5, 9, 14, 11, 15, 7, and 10.
The greatest value is 15 and the least value is 5. So, the range is 15 – 5 or 10.
b. Playing Video Games
Stem
2
3
4
Leaf
6779
014558
269
42 = 42 minutes
The greatest value is 49 and the least value is 26. So, the range is 49 – 26 or 23.
Quartiles – the values that divide the data into four equal parts
Lower Quartile – the median of the lower half of a set of data
Upper Quartile – the median of the upper half of a set of data
Interquartile Range – the difference between the upper quartile and the lower quartile
Example 2
Identify Measures of Variation
The table shows the pounds of paper that differentPounds of Paper
classrooms collected on the first day of a recycling drive. Find the6 11
3 18
7
5 13
9
measures of variation for the data.
RECYCLING
Step 1
Find the range.
18 – 3 or 15 pounds
Step 2
Find the median and the upper and lower quartiles.
Order the data from least to greatest.
median
lower quartile
3
5
6
7
5+6
2 or 5.5
9
7+ 9
2 or 8
upper quartile
11
13
18
11+ 13
or 12
2
The median is 8, the lower quartile is 5.5, and the upper quartile is 12.
Outliers – when a data point is more than 1.5 times the value of the interquartile range beyond
the quartiles.
Example 3
Find Outliers
ROLLER COASTERS Find any outliers in the data set.
Step 1
Find the interquartile range.
lower
quartile

median

upper
quartile

1, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 10
8–6=2
Number of Roller
Coasters Ridden
5
8
9
9
8
7
6
7
1 10
7
5
6
8
7
8
Step 2
Step 3
Multiply the interquartile range, 2, by 1.5.
2  1.5 = 3
Subtract 3 from the lower quartile and add 3 to the upper quartile.
63=3
8 + 3 = 11
The only outlier is 1 because it is less than 3.
Example 4 Use Measures of Variation
LAKES Use the measures of variation to describe
Average Depth of Lakes
the data at the right.
Average
Lake
Find the measures of variation.
The range is 149 – 12 or 137.
The median is 72
The upper quartile is 86.
The lower quartile is 19.
The interquartile range is 86  19 or 67.
Lake Victoria
Lake Superior
Lake Michigan
Great Bear Lake
Lake Ontario
Lake Erie
Lake Winnipeg
Depth (m)
40
149
72
72
86
19
12
The spread of the data is 137 meters. The median is 72 meters. One fourth of the lakes have
an average depth of 19 meters or less. One fourth of the lakes have an average depth of 86
meters or more. Half of the lakes have a depth in the interval 19-86 meters.
Real-World Example 5 Measures of Variation
MARRIAGE The ages at which men and women
first get married are listed in the stem-and-leaf
plot.
a. What is the median age for each group?
The median age for the men is 35. So, one half
men getting married are younger than 35.
Men
9
86332
9765540
62
1
of
4
03 = 30 years
1
2
3
4
5
6
Women
889
011359
247
1
36
7
23 = 23 years
The median age for the women is 27. So, one half of
women getting married are younger than 27.
b. Compare the range of ages for the men and the women.
The range for the men is 64 – 19 or 45 years and the range for the women is 67 – 18
or 49 years. So, the ages vary more for the women than the men.
c. How does the outlier affect the measures of central tendency for the ages of the
women?
Calculate the mean, median, and range without the outlier, 67.
mean:
median:
mode:
without the outlier
18 + 18 + …+ 56
 29.8
16
25
18, 21
with the outlier
18 + 18 + …+ 67
 32.1
16
27
18, 21
The mean increased by 32.1 – 29.8, or 2.3, the median increased by 27 – 25 or 2, and the
mode did not change.
```