Q: Given the following five-number summary for sodium content in cereals: Minimum = 0, Q1 = 135, Median = 180, Q3 = 205, Maximum = 340, what is the interquartile range (IQR)? $$\text{IQR} = Q_3$ - Q_1$

$$\text{IQR} = 205 - 135 = 70$$

Question 1

Which of the following best describes the main difference between a histogram and a bar chart?

Accepted Answer

A histogram displays frequencies for intervals of numerical data, while a bar chart displays frequencies for categories.

Question 2

Given the following five-number summary for sodium content in cereals: Minimum = 0, Q1 = 135, Median = 180, Q3 = 205, Maximum = 340, what is the interquartile range (IQR)?

$$	ext{IQR} = Q_3$ - Q_1$

Accepted Answer

$$	ext{IQR} = 205 - 135 = 70$$

Question 3

A distribution of exam scores is skewed to the right. Which of the following is most likely true about the mean and median?

Accepted Answer

The mean is greater than the median.

Question 4

A box plot is constructed for the sodium content in cereals. According to the 1.5 x IQR rule, which value would be considered a potential outlier?

$$	ext{Lower bound} = Q_1$ - 1.5 	imes 	ext{IQR}$$
$$	ext{Upper bound} = Q_3$ + 1.5 	imes 	ext{IQR}$$

Given $$Q_1 = 135$, Q_3$ = 205$$, $$	ext{IQR} = 70.$$

Accepted Answer

Any value less than $$30 or $$greater than $$310.$$

Question 5

Which of the following measures is most resistant to outliers?

Accepted Answer

Median

Question 6

A student scored 1200 on the SAT (mean = 980, SD = 250) and another scored 24 on the ACT (mean = 20, SD = 5). Who performed better relative to their test's distribution?

$$z = \frac{	ext{observation} - 	ext{mean}}{	ext{standard deviation}}$$

Accepted Answer

The SAT student, because their z-score is higher.

Question 7

Which of the following best describes a bimodal distribution?

Accepted Answer

A distribution with two distinct peaks.

Question 8

Given the following contingency table for food and pesticide status, what is the proportion of organic food with pesticides present?

Organic Present: 29, Organic Total: 127

Accepted Answer

$$\frac{29}{127}$$

Question 9

Which of the following is NOT a property of the standard deviation?

Accepted Answer

It is resistant to outliers.

Question 10

A frequency table is constructed for shark attacks in various regions. What is the main advantage of using a pie chart to display this data?

Accepted Answer

It visually represents the proportion of attacks in each region as parts of a whole.

Question 11

If a dataset has the following values: 3, 7, 6, 8, 5, 5, 7, 5, 9, what is the mode?

Accepted Answer

5

Question 12

Which of the following best describes the meaning of the 90th percentile in a distribution?

Accepted Answer

90% of the observations are below or at this value.

Question 13

A histogram of body fat percentage is shown to be skewed to the right. Which measure of center is most appropriate to describe the typical body fat percentage?

Accepted Answer

Median

Question 14

Which of the following is the correct formula for the sample mean $$\bar{x} of$$ $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

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

Question 15

Which of the following is a valid interpretation of a z-score of -2.5 for a student’s test score?

Accepted Answer

The student scored 2.5 standard deviations below the mean.

Question 16

Which of the following is NOT part of the five-number summary?

Accepted Answer

Mean

Question 17

A bar chart of shark attacks is ordered from largest to smallest frequency. What is the main advantage of this ordering?

Accepted Answer

It makes it easier to compare the relative sizes of the categories.

Question 18

Which of the following is the correct formula for the sample standard deviation $$s of$$ $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$ with mean $$\bar{x}$$?

Accepted Answer

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

Question 19

Which of the following best describes a symmetric distribution?

Accepted Answer

The left and right sides are mirror images of each other.

Descriptive Statistics: Summarizing and Displaying Data

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