Question 1

Which of the following best describes the purpose of a histogram in statistics?

Accepted Answer

To show the distribution of a quantitative variable by grouping data into bins

Question 2

Given a dataset of exam scores, which measure would best describe the 'typical' score if the data is skewed to the right?

Accepted Answer

The median

Question 3

Suppose you have the following five data points: 2, 4, 6, 8, 10. What is the standard deviation of this dataset? Use the formula $$s = \sqrt{\frac{\sum (x_i - \bar{x})^2$}{n-1}}.$$

Accepted Answer

$$s = 2.83$$

Question 4

A researcher wants to compare the heights of male and female students. Which type of graph would be most appropriate for visualizing the distributions of both groups?

Accepted Answer

A side-by-side boxplot

Question 5

If a dataset has a mean of 50 and a standard deviation of 5, what is the z-score for a value of 60? Use the formula $$z = \frac{x - \mu}{\sigma}.$$

Accepted Answer

$$z = 2$$

Question 6

Which of the following statements about boxplots is TRUE?

Accepted Answer

Boxplots are useful for identifying outliers and comparing distributions

Question 7

A sample of 100 patients has a mean cholesterol level of 200 mg/dL and a standard deviation of 20 mg/dL. What percentage of patients are expected to have cholesterol levels between 180 mg/dL and 220 mg/dL, assuming a normal distribution? Use the empirical rule.

Accepted Answer

About 68%

Question 8

Which of the following is NOT a measure of spread?

Accepted Answer

Median

Question 9

A dataset contains the following values: 5, 7, 7, 8, 10. What is the mode of the dataset?

Accepted Answer

7

Question 10

Which scenario best illustrates the use of the interquartile range (IQR)?

Accepted Answer

Measuring the spread of the middle 50% of test scores in a class

Question 11

A hospital administrator wants to summarize the ages of patients admitted in the last month. The ages are: 22, 25, 29, 34, 40, 45, 50, 55, 60, 65. What is the median age?

Accepted Answer

42.5

Question 12

Which of the following is a characteristic of a right-skewed distribution?

Accepted Answer

The mean is greater than the median

Question 13

A pharmaceutical company collects data on the time (in minutes) it takes for a new drug to relieve pain. The data is heavily left-skewed. Which measure of center should the company report?

Accepted Answer

Median

Question 14

Which formula is used to calculate the sample mean $$\bar{x}$$ for a dataset with $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$$

Question 15

A dataset has a mean of 100 and a standard deviation of 15. What is the value that is two standard deviations above the mean?

Accepted Answer

130

Question 16

Which of the following best describes the empirical rule for a normal distribution?

Accepted Answer

About 68% of data falls within one standard deviation of the mean

Question 17

A biologist records the weights of 50 frogs and finds the data is approximately symmetric. Which measure of center and spread should be reported?

Accepted Answer

Mean and standard deviation

Question 18

Which of the following is a valid interpretation of a z-score of $$-1.5$$?

Accepted Answer

The value is 1.5 standard deviations below the mean

Question 19

A nutritionist collects data on daily calorie intake for a group of athletes. The data is bimodal. Which of the following is most likely TRUE?

Accepted Answer

There are two distinct groups with different typical calorie intakes

Question 20

Which of the following is the correct formula for the sample variance $$s^2$$?

Accepted Answer

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

Exploring Data with Graphs and Numerical Summaries

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