Q: A boxplot of Space Mountain wait times shows values of 105 and 110 minutes. If Q₃ = 50 and IQR = 25, which formula determines if these values are outliers?

Values above $$Q_3 + 1.5$$ \times IQR$$ are outliers; 50 + 1.5$$ \times 25 = 87.5$$.

Question 1

Which of the following best describes the difference between a population parameter and a sample statistic?

Accepted Answer

A population parameter describes the entire population, while a sample statistic is calculated from a subset of the population.

Question 2

A researcher wants to estimate the average height of adult males in a city. She collects data from volunteers at a local gym. Which sampling method is being used, and what is a likely pitfall?

Accepted Answer

Convenience sampling; results may be biased because gym-goers may not represent the entire population.

Question 3

Which of the following statements about correlation is TRUE?

Accepted Answer

The correlation coefficient $$r is $$unitless and symmetric, and does not imply causation.

Question 4

Given the following data: 2, 4, 6, 8. Calculate the sample standard deviation using the shortcut formula.

Accepted Answer

$$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} x_i^2$ - \frac{n}{n-1} \bar{x}^2} = \sqrt{\frac{20}{3}} \approx 2.58$$

Question 5

A histogram of exam scores shows a long tail to the right. Which statement best describes the shape and the relationship between mean, median, and mode?

Accepted Answer

The distribution is right-skewed; mode \u003c median \u003c mean.

Question 6

A pharmaceutical company compares the variability of two drugs: Drug A (mean = $$10$$, SD = $$2) $$and Drug B (mean = $$100$$, SD = $$15). $$Which drug is more consistent, and what measure supports your answer?

Accepted Answer

Drug B is more consistent; its coefficient of variation is lower.

Question 7

Which formula is used to calculate the z-score for a sample data value $$x$$?

Accepted Answer

$$z = \frac{x - \bar{x}}{s} $$

Question 8

A boxplot of Space Mountain wait times shows values of 105 and 110 minutes. If Q₃ = 50 and IQR = 25, which formula determines if these values are outliers?

Accepted Answer

Values above $$Q_3 + 1.5$$ 	imes IQR$$ are outliers; 50 + 1.5$$ 	imes 25 = 87.5$$.

Question 9

Which measure of center is most resistant to outliers, and why?

Accepted Answer

The median, because it is the middle value and not affected by extreme values.

Question 10

A dataset has values: 10, 12, 13, 14, 16. What is the range, and what does it tell you about the spread?

Accepted Answer

Range is $$16 - 10 = 6$$; it uses only two values and may not reflect overall spread.

Question 11

If a dataset is transformed by adding 5 to every value, what happens to the standard deviation?

Accepted Answer

The standard deviation remains unchanged.

Question 12

Which of the following is NOT a pitfall in drawing statistical conclusions?

Accepted Answer

Using random sampling.

Question 13

A frequency distribution table shows cumulative frequency reaching 100 at the last class. What does this indicate?

Accepted Answer

The cumulative frequency represents the total number of data points.

Question 14

Which formula gives the coefficient of variation (CV) for a sample?

Accepted Answer

$$CV = \frac{s}{\bar{x}} 	imes 100\% $$

Question 15

A scatterplot shows points clustered along a straight line with a positive slope. The correlation coefficient is $$r = 0.85. $$How would you interpret this?

Accepted Answer

There is a strong positive linear relationship between the variables.

Question 16

Which formula is used to calculate the sample variance?

Accepted Answer

$$s^2$$ = \frac{\sum_{i=1}^{n} (x_i - \bar{x}$$)^2$$}{n-1} $$

Question 17

A value in a dataset has a z-score of $$z = 2.5. $$What does this indicate about the value?

Accepted Answer

It is significantly higher than the mean, since $$|z| \u003e 2.$$

Question 18

Which measure should you use to compare the variability of two datasets with different units (e.g., dollars vs. centimeters)?

Accepted Answer

Coefficient of variation.

Question 19

In a frequency distribution, what is the class midpoint for a class with lower limit 10 and upper limit 20?

Accepted Answer

$$\frac{10 + 20}{2} = 15$$

Introductory Statistics Exam 1 Study Guide: Major Topics and Concepts

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