7th Grade Math

Lesson 2A Measures of Variation 499

Find Measures of Variation

SPEED Find the measures

of variation for the data.

Range 70 - 1 or 69 mph

Quartiles

Order the numbers from

least to greatest.

lower half median upper half

⎩   ⎨   ⎧

⎩^ ^ ^ ⎨^ ^ ^ ⎧^

1 8 25 30 50 70

⎧ ⎨ ⎩

LQ _^25 + 2 30 = 27.5 UQ

Interquartile Range 50 - 8 or 42 UQ - LQ

The range is 69, the median is 27.5, the lower quartile is 8, the

upper quartile is 50, and the interquartile range is 42.

a. SPORTS Determine the measures

Basketball Scores

64 61 67 59 60

of variation for the data in the table.^5857715662

An outlier is a data value that is either much greater or much less than

the median. If a data value is more than 1.5 times the value of the

interquartile range beyond the quartiles, it is an outlier.

Find Outliers

ELECTIONS The ages of candidates in an election are 23, 48, 49, 55,

57, 63, and 72. Name any outliers in the data.

Find the interquartile range.

63 - 48 = 15

Multiply the interquartile range by 1.5.

15 × 1.5 = 22.5

Subtract 22.5 from the lower quartile and add 22.5 to the upper

quartile.

48 - 22.5 = 25.5 63 + 22.5 = 85.5

The limits for the outliers are between 25.5 and 85.5. The only age

beyond this is 23. So, it is the only outlier.

b. BRIDGES The lengths, in feet, of various bridges are 88, 251, 275,

354, and 1,121. Name any outliers in the data set.

Interquartile Range Interquartile Range If the

interquartile range is low,

the middle data are

grouped closely together.

Real-World Link

The 26th Amendment

to the United States

Constitution lowered

the voting age to 18.

RRR

T

Animal Speeds

50

30

25

8

1

70

elephant

mouse

spider

cheetah

lion

cat

Animal Speed (mph)

498_509_C09_L2_895130.indd 499 1/11/10 9:34 AM