Main Idea and New Vocabulary

Key Concept: Using Mean, Median, and Mode

Example 1: Choose an Appropriate Measure

Example 2: Choose the Appropriate Measure

Example 3: Choose the Appropriate Measure

Example 4: Choose the Appropriate Measure

• Choose an appropriate measure of central tendency. Identify outliers.

• outlier

Choose an Appropriate Measure

SEA TURTLES The table shows the total number of sea turtles observed at four sea turtle research sites on the eastern coast of Florida. Which measure of central tendency best represents the data? Find that measure of central tendency.

Since the set of data has an extreme value, 207, and no repeated values, the median would best represent the data.

Choose an Appropriate Measure

207 1,033 1,231 1,332

Answer: The median number of sea turtles observed is 1,132.

A. mean; $4.69

B. median; $4.38

C. mode; $4.75

D. mode; $4.50

SANDWICHES The prices of several sandwiches are $4.50, $4.75, $4.50, $4.25, $4.50, $4.50, $5.75, and $4.75. Which measure of central tendency best represents the data? Find that measure of central tendency.

ANIMALS The table shows the number of threatened species in the United States in 2005. Identify the outlier in the data set.

Compared to the other values, 43 is extremely high.

Choose the Appropriate Measure

Answer: So, the outlier is 43.

A. 53°

B. 75°

C. 78°

D. 83°

WEATHER The daily high temperatures for one week were 78°, 75°, 53°, 75°, 79°, 83°, and 76°. Identify the outlier in the set.

Choose the Appropriate Measure

ANIMALS The table shows the number of threatened species in the United States in 2005. Determine how the outlier affects the mean, median, and mode of the data.

Find the mean, median, and mode with and without the outlier.

With the outlier

Choose the Appropriate Measure

Median 11

Mode 9 and 11

Without the outlier

Median 10

Mode 9 and 11

Answer: The mean decreased by 15 – 10 or 5. The median decreased by 1. The mode did not change.

Choose the Appropriate Measure

A. mean: decreased by about 3.5; median: increased by 1; mode: no change

B. mean: increased by about 3.5; median: increased by 1; mode: no change

C. mean: increased by about 3.5; median: decreased by 1; mode: no change

D. mean: decreased by about 3.5; median: no change; mode: no change

WEATHER The daily high temperatures for one week were 78°, 75°, 53°, 75°, 79°, 83°, and 76°. Determine how the outlier affects the mean, median, and mode of the data.

ANIMALS The table shows the number of threatened species in the United States in 2005. Which measure of central tendency best describes the data with and without the outlier?

The mean with the outlier is 15 and without the outlier is 10.

Choose the Appropriate Measure

The median with the outlier is 11 and without the outlier is 10.

The modes were 9 and 11 both with and without the outlier.

The mean was affected the most with the outlier.

The median changed very little with and without the outlier.

The modes do not describe the data very well since there were only two repeated numbers.

Choose the Appropriate Measure

Answer: The median best describes the data sinceit changed very little with and without theoutlier.

A. The mean best describes the data because it changed very little with and without the outlier.

B. The median best describes the data because it changed very little with and without the outlier.

C. The mode best describes the data because there are two repeated numbers.

WEATHER The daily high temperatures for one week were 78°, 75°, 53°, 75°, 79°, 83°, and 76°. Which measure of central tendency best describes the data with and without the outlier? Justify your selection.