Question 1

Refer to the ogive graph showing goals scored by winning teams in a football tournament final. What score represents the 60th percentile, and what does this mean in the context of the tournament?

Accepted Answer

The 60th percentile corresponds to 4 goals. This means that 60% of the winning teams scored 4 goals or fewer, and 40% scored more than 4 goals.

Question 2

Given the wait times (in minutes) for a theme park ride: 12, 18, 22, 28, 30, 34, 40, 48, 52, 170. Calculate the mean and median with and without the outlier (170). How are the mean and median affected by the outlier?

Accepted Answer

With outlier: Mean = 31.6, Median = 32.0; Without outlier: Mean = 45.4, Median = 32.0. The mean decreased significantly, while the median changed only slightly, showing the median is more resistant to outliers.

Question 3

An investment fund experienced annual growth rates of 1.2%, 0.9%, 1.5%, 0.7%, and 1.1% over 5 years. What is the geometric mean growth rate, expressed as a percentage?

Accepted Answer

$$1.05\%$$

Question 4

Given the workout durations (in minutes): 30, 45, 60, 50, 40, 55, 70, 35, 65, 50, 42, calculate the range, variance, and standard deviation. What do these results tell us about the variation in workout durations?

Accepted Answer

Range = 40 minutes, Variance = 155.8 minutes$$^2$$, Standard deviation = 12.48 minutes. The workout durations show moderate variability, meaning they are somewhat spread out but not extremely different.

Question 5

Which boxplot correctly represents the ages (in years) of the workshop participants: 22, 25, 28, 21, 24, 27, 23, 26, 29, 22, 25, 28, 24, 27, 14?

Accepted Answer

Boxplot in image 1 (first boxplot shown above)

Question 6

A group of hikers recorded the distances they covered during a week: 7, 9, 11, 12, 14, 15, 17, 18, 20, 21. For the original and 10% trimmed data set, what are the mean, median, mode, and midrange?

Accepted Answer

Mean: 14.5 (both); Median: 14.5 (original), 14 (trimmed); Mode: None (both); Midrange: 14.5 (original), 14 (trimmed)

Question 7

You are evaluating year-end bonus trends at two potential employers. Companies X and Y have an average bonus of $$5,000, with standard deviations of 800 $$and $$500, respectively. If you aim to receive a bonus of 6$$,000 or higher, at which company is that outcome more likely, and why?

Accepted Answer

Company X, because its bonuses vary more and have a higher chance of reaching $6,000.

Question 8

Given the weights (in kg) of 12 randomly selected backpacks: 7, 12, 9, 15, 20, 17, 11, 14, 10, 9, 12, 9. Find $$Q_1$$, $$Q_2$$, and $$Q_3.$$

Accepted Answer

$$Q_1 = 9$, Q_2$ = 11.5$$, $$Q_3 = 14.5$

Question 9

Suppose a data set is highly skewed to the right. Which measure of central tendency is most likely to be greater than the others?

Accepted Answer

Mean

Question 10

A researcher collects the following data on the number of hours students study per week: 5, 7, 8, 10, 12, 15, 20. If the researcher wants to describe the spread of the data, which measure should they use and why?

Accepted Answer

Standard deviation, because it measures the average distance of data points from the mean.

Question 11

If a data set has a range of 40, a variance of 155.8, and a standard deviation of 12.48, what is the formula for standard deviation in terms of variance?

Accepted Answer

$$s = \sqrt{	ext{variance}}$$

Question 12

A boxplot is used to display which of the following features of a data set?

Accepted Answer

The five-number summary: minimum, $$Q_1$$, median, $$Q_3$$, and maximum.

Statistics Exam 2 Study Guide: Percentiles, Measures of Center, Variability, Boxplots, and More

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