Question 1

Which of the following best describes the difference between numerical and categorical variables?

Accepted Answer

Numerical variables represent quantities that can be measured, while categorical variables represent groups or categories.

Question 2

Given a data set with columns: 'Age', 'Gender', 'Income', and 'Favorite Color', which of the following can be inferred from the variable names alone?

Accepted Answer

The data set contains both numerical and categorical variables.

Question 3

A histogram of exam scores shows a single peak near the middle and tails that extend further to the left than to the right. Which best describes the shape of the distribution?

Accepted Answer

Unimodal and left-skewed

Question 4

If a histogram has bins of width 5 and the tallest bin covers scores from 70 to 75, what does this indicate about the mode of the data?

Accepted Answer

The mode is in the interval 70 to 75.

Question 5

Given the data points: 2, 4, 6, 8, 10. What is the mean and standard deviation of this data set?

Accepted Answer

Mean: $$6$$, Standard deviation: $$\sqrt{10}$$

Question 6

If you add a new data point (12) to the set {2, 4, 6, 8, 10}, how will the mean and standard deviation change?

Accepted Answer

The mean will increase and the standard deviation will increase.

Question 7

A set of running times has a mean of 50 minutes and a standard deviation of 5 minutes. According to the Empirical Rule, approximately what percentage of times fall between 45 and 55 minutes?

Accepted Answer

About 68%

Question 8

A data set of running times has a mean of 50 minutes and a standard deviation of 5 minutes. According to the Empirical Rule, what interval contains approximately 95% of the data?

Accepted Answer

$$[40, 60]$$

Question 9

Given the following pairs of values: (1,2), (2,4), (3,6), (4,8), (5,10), what is the association between x and y?

Accepted Answer

Linear and positive

Question 10

Given the data pairs: (1,2), (2,4), (3,6), (4,8), (5,10), what is the regression equation $$y = ax + b$$?

Accepted Answer

$$y = 2x$$

Question 11

A scatterplot shows points forming a downward trend from left to right. Which best describes the association between the variables?

Accepted Answer

Negative linear association

Question 12

A scatterplot shows points clustered in a curve that rises and then falls. Which best describes the association?

Accepted Answer

Nonlinear association

Question 13

Given TI-84 regression output: Slope = 1.5, y-intercept = 2. What is the regression equation?

Accepted Answer

$$y = 1.5x + 2$$

Question 14

If the regression equation is $$y = -0.8x + 10$$, what does the slope indicate about the relationship between x and y?

Accepted Answer

For each unit increase in x, y decreases by 0.8 units.

Question 15

A histogram of cholesterol levels in a population is bimodal. What does this suggest about the population?

Accepted Answer

There are two distinct groups with different typical cholesterol levels.

Question 16

If a data set has a mean of 100 and a standard deviation of 15, what percentage of data is expected to fall between 85 and 115 according to the Empirical Rule?

Accepted Answer

About 68%

Question 17

A data set of exam scores has a mean of 80 and a standard deviation of 10. If a student scores 100, how many standard deviations above the mean is this score?

Accepted Answer

$$\frac{100 - 80}{10} = 2$$

Question 18

If a regression equation is $$y = 3x + 5$$, what is the predicted value of y when x = 4?

Accepted Answer

$$y = 3 	imes 4 + 5 = 17$$

Question 19

A data set of heights is right-skewed. Which statement is most likely true?

Accepted Answer

The mean is greater than the median.

Introductory Statistics Midterm Study Guide – Step-by-Step Guidance

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