Question 1

Which of the following best describes the difference between descriptive statistics and inferential statistics?

Accepted Answer

Descriptive statistics summarize and organize data, while inferential statistics draw conclusions about a population based on a sample.

Question 2

A baseball researcher wants to test if the thickness of red laces affects the number of home runs in a season. She randomly selects 20 MLB games and compares home runs using two types of baseballs. What type of statistics is she using?

Accepted Answer

Inferential statistics

Question 3

Which of the following is NOT a measure of central tendency?

Accepted Answer

Variance

Question 4

Given the data set: 2, 4, 6, 8, 10, what is the sample mean $$\bar{x}$$?

Accepted Answer

$$\bar{x} = \frac{2+4+6+8+10}{5} = 6$$

Question 5

Which of the following variables collected at a football stadium is qualitative?

Accepted Answer

Jersey color

Question 6

What is the main purpose of a relative frequency table?

Accepted Answer

To relate counts to the total number of observations

Question 7

A pie chart is most appropriate when:

Accepted Answer

There are fewer than 5 categories and percentages are not too small

Question 8

Which of the following graphs is most likely to be misleading due to improper scaling?

Accepted Answer

A bar chart where the y-axis does not start at zero

Question 9

In a stem-and-leaf diagram, what does the 'stem' represent?

Accepted Answer

The tens digit or higher place values of each value

Question 10

Which distribution shape is described as 'symmetric'?

Accepted Answer

The right and left sides of the distribution are mirror images of each other

Question 11

If the mean is to the right of the median in a distribution, the data is:

Accepted Answer

Positively skewed

Question 12

Which sampling method is most likely to introduce bias if you estimate the average weight of all adult males using only professional football players?

Accepted Answer

Convenience sampling

Question 13

What is the formula for sample standard deviation $$s$$?

Accepted Answer

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

Question 14

A box plot is especially useful for:

Accepted Answer

Comparing two or more data sets

Question 15

If a value is more than $$1.5 	imes$$ the interquartile range (IQR) from the edge of the box in a box plot, it is considered:

Accepted Answer

A potential outlier

Question 16

Which of the following is a real-world example of continuous quantitative data?

Accepted Answer

Length of a foot measured in centimeters

Question 17

In stratified random sampling with proportional allocation, if a town has 250 homeowners (25 upper income, 175 middle income, 50 low income) and you want a sample of 20, how many should be selected from the middle income group?

Accepted Answer

14

Question 18

What is the trimmed mean and why is it used?

Accepted Answer

The mean after removing a certain percentage of values from both ends of the data set; it is used to reduce the effect of outliers.

Question 19

Which of the following is NOT a common error that can make a graph misleading?

Accepted Answer

Labeling axes clearly

Question 20

According to the Empirical Rule, approximately what percentage of data lies within two standard deviations of the mean in a normal distribution?

Accepted Answer

95%

Unit 1: Foundations of Elementary Statistics – Data, Sampling, and Descriptive Measures

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