Mean Scores and Outliers: A 6th Grade Challenge

A class of 5 students scored the following on a test: 85, 90, 78, 92, and 100. What is the mean score? Are there any outliers affecting the mean?

• The mean score is 91, and there are no outliers affecting the mean.

• The mean score is 90, and there is one outlier affecting the mean.

• The mean score is 89, and there are no outliers affecting the mean.

• The mean score is 88, and there are two outliers affecting the mean.

In a basketball game, Player A scored 20, 22, 19, 30, and 25 points in five games. What is the mean score? How does this compare to Player B, who scored 15, 18, 20, 25, and 50 points?

• Player A's mean score is 25.0; Player B's mean score is 20.0.

• Player A's mean score is 21.0; Player B's mean score is 30.0.

• Player A's mean score is 22.5; Player B's mean score is 24.0.

• Player A's mean score is 23.2; Player B's mean score is 25.6.

The heights (in inches) of five plants are: 12, 14, 15, 13, and 100. Calculate the mean height. Is the 100-inch plant an outlier? How does it affect the mean?

• Mean height is 50 inches; the 100-inch plant is an outlier and has no effect on the mean.

• Mean height is 30.8 inches; the 100-inch plant is an outlier and affects the mean by increasing it.

• Mean height is 20 inches; the 100-inch plant is not an outlier and does not affect the mean.

• Mean height is 25 inches; the 100-inch plant is an outlier but decreases the mean.

A store sells packs of gum for $1, $2, $3, $4, and $10. What is the mean price of a pack of gum? Discuss how the $10 pack affects the mean compared to the other prices.

• $3

• $5

• $4

• $6

In a science experiment, the weights (in grams) of five samples are: 50, 52, 48, 49, and 100. What is the mean weight? Identify any outliers and explain their impact on the mean.

• Mean weight is 60 grams; outlier is 49 grams.

• Mean weight is 59.8 grams; outlier is 100 grams.

• Mean weight is 55 grams; outlier is 48 grams.

• Mean weight is 50 grams; outlier is 52 grams.

Two friends recorded their weekly exercise hours: Friend 1: 5, 6, 7, 8, 9 hours; Friend 2: 4, 5, 6, 7, 50 hours. What are the means for both friends? How does the outlier in Friend 2's data affect the comparison?

• Friend 1 mean: 7 hours, Friend 2 mean: 14.4 hours; outlier affects comparison by inflating Friend 2's mean.

• Friend 1 mean: 6 hours, Friend 2 mean: 10 hours; outlier has no effect.

• Friend 1 mean: 7.5 hours, Friend 2 mean: 15 hours; outlier makes comparison irrelevant.

• Friend 1 mean: 8 hours, Friend 2 mean: 20 hours; outlier decreases Friend 2's mean.

A teacher recorded the number of books read by students in a month: 3, 4, 5, 2, and 20. What is the mean number of books read? Is there an outlier? How does it influence the mean?

• The mean number of books read is 6.8, and there is an outlier (20) that influences the mean.

• The mean number of books read is 10, and there is an outlier (4).

• The mean number of books read is 8, and the outlier is 5.

• The mean number of books read is 5, and there is no outlier.

In a survey, the ages of participants are: 12, 13, 14, 15, and 100. Calculate the mean age. Discuss whether the 100-year-old participant is an outlier and its effect on the mean.

• The mean age is 25, and the 100-year-old participant is a typical participant.

• The mean age is 50, and the 100-year-old participant is an average age.

• The mean age is 20, and the 100-year-old participant is not an outlier.

• The mean age is 30.8, and the 100-year-old participant is an outlier that skews the mean.

The daily temperatures (in degrees) for a week were: 70, 72, 68, 71, and 100. What is the mean temperature? Identify any outliers and their effect on the mean temperature.

• Mean temperature is 72; outlier is 68.

• Mean temperature is 75; outlier is 71.

• Mean temperature is 80; outlier is 72.

• Mean temperature is 76.2; outlier is 100.

A group of friends recorded their monthly spending: $200, $250, $300, $400, and $1000. What is the mean spending? Discuss how the $1000 affects the overall mean compared to the other amounts.

• 430

• 600

• 500

• 350