Holt CA Course 1

7-2 Additional Data and Outliers

SDAP1.2 Understand how additional data added to data sets may affect these computations.Also covered: SDAP1.1, SDAP1.3

California Standards

Holt CA Course 1

7-2 Additional Data and Outliers

Vocabulary

outlier

Holt CA Course 1

7-2 Additional Data and Outliers

The mean, median, mode, and range may change when you add data to a data set.

Holt CA Course 1

7-2 Additional Data and OutliersAdditional Example 1A: Sports Application

Find the mean, median, mode, and range of the data in the table.

EMS Football Games Won

Year 1998 1999 2000 2001 2002

Games 11 5 7 5 7

median: Write the data in numerical order: 5, 5, 7, 7, 11.

range: 11 – 5 = 6

mean: 11 + 5 + 7 + 5 + 7 5

= 7

mode: 5, 7 The values 5 and 7 occurs most often.

Subtract the least value from the greatest value.

Holt CA Course 1

7-2 Additional Data and Outliers

Additional Example 1B: Sports Application

EMS also won 13 games in 1997 and 8 games in 1996. Add this data to the data in the table and find the mean, median, mode, and range.

mean: 9

median: 7

modes: 5, 7

range: 8

The mean increased by 2.

The median stayed the same.

The modes stayed the same.

The range increased by 2.

Holt CA Course 1

7-2 Additional Data and OutliersCheck It Out! Example 1A

Find the mean, median, mode, and range of the data in the table.

median: Write the data in numerical order: 4, 6, 6, 11, 13.

range: 13 – 4 = 9

mean: 13 + 6 + 4 + 6 + 11 5

= 8

mode: 6 The value 6 occurs most often.

Subtract the least value from the greatest value.

MA Basketball Games Won

Year 1998 1999 2000 2001 2002

Games 13 6 4 6 11

Holt CA Course 1

7-2 Additional Data and OutliersCheck It Out! Example 1B

mean: 9

median: 8

mode: 6

range: 11

The mean increased by 1.

The median increased by 2.

The mode stayed the same.

The range increased by 2.

MA also won 15 games in 1997 and 8 games in 1996. Add this data to the data in the table and find the mean, median, and mode.

Holt CA Course 1

7-2 Additional Data and Outliers

An outlier is a value in a set that is very different from the other values. One way to identify an outlier is by making a line plot. A line plot uses a number line and x’s or other symbols to show the frequencies of values.

Holt CA Course 1

7-2 Additional Data and OutliersAdditional Example 2: Identifying Outliers

Television Prices

$141 $225 $849 $246

$269 $165 $258 $159

Step 1: Draw a number line.

Step 2: For each television price, use an on the number line to represent its price in dollars.

100 200 300 400 500 600 700 800 900

The table shows the prices of television sets at a discount store. Which price represents an outlier?

Prices of Televisions ($)

The line plot shows that the value 849 is much greater than the other values in the set. The price of 849 represents an outlier.

Holt CA Course 1

7-2 Additional Data and OutliersCheck It Out! Example 2

Length of Hair Cuts (in.)

12 3 4 2

2 1 4 1

Step 1: Draw a number line.

Step 2: For each length, use an on the number line to represent its length in inches.

1 2 3 4 5 6 7 8 9 10 11 12

Length of Hair Cuts (in.)

The table shows the number of inches of hair cut from a salon's last eight customers. Which length represents an outlier?

The line plot shows that the value 12 is much greater than the other values in the set. The length of 12 represents an outlier.

Holt CA Course 1

7-2 Additional Data and OutliersAdditional Example 3: Application

Ms. Gray is 25 years old. She took a class with students who were 55, 52, 59, 61, 63, and 58 years old. Find the mean, median, mode, and range with and without Ms. Gray’s age.

mean: 53.3 mode: none median: 58 range: 38

mean: 58 mode: none median: 58.5 range: 11

When you add Ms. Gray’s age, the mean decreases by about 4.7, the mode stays the same, the median decreases by 0.5, and the range increases by 27. The mean and the range are most affected by the outlier.

Data with Ms. Gray’s age:

Data without Ms. Gray’s age:

Holt CA Course 1

7-2 Additional Data and OutliersCheck It Out! Example 3

Ms. Pink is 56 years old. She volunteered to work with people who were 25, 22, 27, 24, 26, and 23 years old. Find the mean, median, mode, and range with and without Ms. Pink’s age.

mean: 29 mode: none median: 25 range: 34

mean: 24.5 mode: none median: 24.5 range: 5

When you add Ms. Pink’s age, the mean increases by 4.5, the mode stays the same, the median increases by 0.5, and the range increases by 29. The mean and the range are most affected by the outlier.

Data with Ms. Pink’s age:

Data without Ms. Pink’s age: