Stats Mini Lesson

How would you describe this graph? 

• Symmetric
• Skewed Right
• Skewed Left
• Bimodal

Two sections of a class took the same quiz.  Section A had 15 students who had a mean score of 80, and section B had 20 students who had a mean score of 90.  Overall, what was the approximate mean score for all students on the quiz?

• A. 84.3
• B. 85.0
• C. 85.7
• D. None of these

What does μ stand for?

• Population standard deviation
• Population mean
• Sample standard deviation
• Sample mean

What does σ stand for?

• Population standard deviation
• Population mean
• Sample standard deviation
• Sample mean

What does x̄ stand for?

• Population standard deviation
• Population mean
• Sample standard deviation
• Sample mean

The time, in minutes, it took each of 11 students to complete a puzzle was recorded and is shown in the following list.

9, 17, 20, 21, 27, 29, 30, 31, 32, 35, 58

One of the students who completed the puzzle claimed that there were two outliers in the data set. Based on the 1.5 × IQR rule for outliers, is there evidence to support the student’s claim?

• Yes, there are two outliers. One outlier is 9 minutes and the other outlier is 58 minutes.

• No, there is only one outlier at 9 minutes.

• No, there is only one outlier at 58 minutes.

• No, there are three outliers. One outlier is 9 minutes, one outlier is 35 minutes, and one outlier is 58 minutes.

• No, there are no outliers.

A reporter collected data on the purchase prices, in thousands of dollars, of 72 cars sold in a region. The above histogram summarizes the reporter’s data.

For a presentation on the data collected, the reporter used the median of the distribution to describe the typical purchase price. Which of the following might explain the use of median to describe the typical purchase price?

• There is an outlier between $80,000 and $85,000. Medians are resistant to outliers, while means are not.

• The number of observations that fall within a given interval is known. However, within each interval, the actual values are not known.

• The distribution is left skewed.

• The values represented in the histogram are in the thousands.

• The distribution is uniform.

The distribution of 27 salaries at a small company has mean $35,000 and standard deviation $2,000. Suppose the company hires a 28th employee at a salary of $120,000. Which of the following claims about the new salary distribution is supported?

1) The median is not likely to change.

2) The range is not likely to change.

3) The mean is likely to increase.

• 1 only

• 3 only

• 1 and 2 only

• 1 and 3 only

• 1, 2 and 3

The above boxplot summarizes the heights of a group of people who participate in a weekend biking club.

Which of the following statements is supported by the boxplot?

• The mean height is 67 inches.

• The number of people with height at least 70 inches is greater than the number of people with height at most 62 inches.

• The number of people with height at least 67 inches is less than the number of people with height at most 67 inches.

• Approximately 50% of the people have a height between 62 inches and 70 inches.

• Approximately 25% of the people have a height greater than 62 inches.

The following boxplot summarizes the earnings made on one day at 45 movie theaters. Which of the following best compares the median movie theater earnings with the mean movie theater earnings?

• The median and mean are equal because the distribution is likely symmetric.

• The median and mean are equal because the distribution is likely skewed to the right.

• The median is less than the mean because the distribution is likely symmetric.

• The median is less than the mean because the distribution is likely skewed to the right.

• The median is less than the mean because the distribution is likely skewed to the left.