# 6th Grade - How Far Away Points Change Things

 Grade Level: 6th Skill: Range, Mean, Median, Mode, Outliers and Central Tendency Topic: How Far Away Points Change Things Goal: Understand how the inclusion or exclusion of outliers affects measures of central tendency. Skill Description: Know that in a data set, an outlier is a number that is numerically distant from the rest of the numbers in a data set. This is, it is far below or far above the middle percent of the data terms. For example, the number 99 is an outlier in the data set: 5, 4, 13, 11, 15, and 99. Understand that using an outlier can cause statistical data to be misleading. The mean will always be affected most by an outlier. For example, if you were asked to find the typical age of people on a playground and used the data set above to calculate the mean, the outlier would completely skew your view of the age. Using the measure of the median age and including the outlier would give you a more accurate view of the typical age. So, the outlier could be excluded to find the mean in this example, or it could be included in using the median. Logic will need to be called upon to decide whether to include or exclude an outlier for a given measure of central tendency.

## Building Blocks/Prerequisites

### Sample Problems

 (1) Determine if the statement below is true or false. The average salary of an employee at J.M. Mills is \$1767 per month. Salaries: \$100, \$150, \$200, \$100, \$50, \$10,000 (false) (2) What measure could best be used to find the typical salary of employees at J.M. Mills, without excluding the outlier, if the salaries are \$100, \$150, \$200, \$100, \$50, \$10,000. (median) (3) What measure could be used to determine the average salary at J.M. Mills if the outlier were excluded if the salaries are \$100, \$150, \$200, \$100, \$50, \$10,000? (mean) (4) Rick’s science scores were: 88, 98, 75, 80 and 0. How will the outlier affect his grade if his teacher averages his scores? What measure of central tendency could be used to find his typical science grade with the outlier included? (The outlier will bring his grade down. The median could be used to find his typical grade.) (5) Carolina was charting the weather in June. Which temperature will most affect the mean when she calculates the average temperature? 77, 78, 79, 78, 78, 110, 80, 84, 82, and 78 (110, it is an outlier.)

### Online Resources

 (1) (2) (3) (4) (5)

### Extra Help Problems

(1)

Identify the outlier in the data set below.

26, 35, 45, 28, 42, 39, 22, 42, 36, 37, 40, 128, 24, 32, 22

(128)

(2)

Identify the outlier in the data set below.

13, 17, 12, 19, 16, 11, 10, 1, 18, 17, 11, 12, 15

(1)

(3)

Identify the outlier in the data set below.

1.4, 1.56, 1.198, 5.1, 2.2, 1.34, 2.12, 2.51, 1.3

(5.1)

(4)

Identify the outlier in the data set below.

-16, 19, 0, -4, -6, -7, -15, -10, -12, 1

(19)

(5)

Identify the outlier in the data set below.

122, 163, -17, 99, 182, 110, 144, 152, 171

(-17)

(6)

Determine which measures of central tendency would change, if you were to first calculate each measure without the outlier and then add it in.

Data Set: 19, 21, 23, 18, 3, 19

(mean 20, median 19, mode 19; mean 17.2, median 19, mode 19)

(7)

Determine which measures of central tendency would change, if you were to first calculate each measure without the outlier and then add it in.

Data Set: 1.1, 1.2, 1, 1.3, -1.5, 1.2

(mode and median)

(8)

Determine which measures of central tendency would change, if you were to first calculate each measure without the outlier and then add it in.

Data Set: 80, 97, 42, 100, 85, 85

(mode)

(9)

Determine which measures of central tendency would change, if you were to first calculate each measure without the outlier and then add it in.

Data Set: 421, 400, 230, 432, 417, 450, 400

(mean, median)

(10)

Determine which measures of central tendency would change, if you were to first calculate each measure without the outlier and then add it in.

Data Set: 52, 56, 59, 58, -2, 62, 58, 58

(mean)

(11)

Find the mean, median, mode and range of the data set with and without the outlier.

5, 7, 9, 10, 5, 24

(mean, median, mode with: 10, 8, 5; without: 7.2, 7, 5)

(12)

Find the mean, median, mode and range of the data set with and without the outlier. Round the mean to the nearest one.

90, 85, 20, 75, 80, 85, 85

(mean, median, mode with: 75, 85, 85; without 83, 85, 85)

(13)

Find the mean, median, mode and range of the data set with and without the outlier.

230, 100, 250, 212, 216

(14)

Find the mean, median, mode and range of the data set with and without the outlier. Round the mean to the nearest tenth.

1.25, 1.5, 1.25, 1.30, 4.50, 1.80

(with: 1.9, 1.4, 1.25; without: 1.42, 1.3, 1.25)

(15)

Find the mean, median, mode and range of the data set with and without the outlier.

-12, 5, 7, 9, 5, 8, 5, 7

(with: 4.25, 6, 5; without: 7.7, 7, 5)

(16)

Saul has been keeping track of the points he’s scored in each basketball game this season in the table below. Use the data to find his average and median score for the games so far. How will these change if he scores 52 points in the next game? Round the average to the nearest one.

 Game 1 Game 2 Game 3 Game 4 Game 5 Game 6 30 points 28 points 26 points 32 points 26 points 30 points

(so far: 29, 29; with 52 points: 32, 30)

(17)

Jesse’s Math scores for the second trimester are: 50, 55, 50, 65, 60, 60. What is her average score for math? What will happen to Jesse’s average if she gets a score of 100 on the next test? Write scores as the nearest percent.

(57%, 63%)

(18)

Claudia is playing a game with her sister. The table shows her scorecard for each round. What is Claudia’s score range? Median? Mode? Mean?

How will these change if she scores 150 points in the last round?

 Round 1 65 Round 2 70 Round 3 70 Round 4 85 Round 5 90

(without 150: median 70, mode 70, mean 76; with 150: median 77.5, mean 70, mode 88)

(19)

Brendan has recorded the height of his puppy, Chino for the first five months he owned him. He wrote down: 1.2 ft, 1.5 ft, 1.5 ft, 1.7 ft, 2 ft. He then recorded his height again at two years as 3.5 feet. Explain how the last measurement would affect each of the measures of central tendency.

(The last height would make the mean increase.)

(20)

Monica has a summer dog-walking job. She’s recorded her earnings as: \$4.50, \$5.25, \$5.25, \$6.50, \$6.25, \$8.00, \$7.50 and \$25.00. How did her last week’s earnings affect the mean and median of the monies she earned over the summer.

(Her mean and median increased.)