Q: Which formula correctly calculates the range of a data set?

$$\text{Range} = \text{max} - \text{min}$$

Question 1

Which of the following is the best graphical display for summarizing the distribution of a categorical variable such as 'Ticket Class' on the Titanic?

Accepted Answer

Bar Chart

Question 2

A frequency table for the variable 'Ticket Class' on the Titanic shows the counts for each class. What does a relative frequency table show instead?

Accepted Answer

The percentage of observations in each category

Question 3

Which of the following statements about pie charts is TRUE?

Accepted Answer

Each slice in a pie chart represents a category, and its size is proportional to the whole.

Question 4

A Pareto chart is a special type of bar chart. What distinguishes a Pareto chart from a regular bar chart?

Accepted Answer

Bars are arranged from most frequent to least frequent, often with a cumulative line.

Question 5

Which of the following is NOT an appropriate way to describe a histogram?

Accepted Answer

Percentage of each category

Question 6

A histogram of ages on the Titanic shows a single central hump. What is the correct term for this type of distribution?

Accepted Answer

Unimodal

Question 7

If a histogram has a long tail stretching to the right, how would you describe its shape?

Accepted Answer

Skewed right

Question 8

Which measure of center is most appropriate for a distribution that is highly skewed with outliers?

Accepted Answer

Median

Question 9

Given the following ordered data set: 2, 4, 5, 6, 7, 9, 9. What is the median?

Accepted Answer

$$6$$

Question 10

The mean of a data set is calculated as $$\bar{y} = \frac{\sum y}{n}. $$Which of the following statements is TRUE about the mean?

Accepted Answer

It is sensitive to outliers.

Question 11

Which formula correctly calculates the range of a data set?

Accepted Answer

$$	ext{Range} = 	ext{max} - 	ext{min}$$

Question 12

The interquartile range (IQR) is calculated as:

Accepted Answer

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

Question 13

Which of the following is a disadvantage of using the range as a measure of spread?

Accepted Answer

It can be made very large by a single extreme value.

Question 14

The standard deviation $$s of a $$data set is calculated using the formula $$s = \sqrt{\frac{\sum (y - \bar{y})^2$}{n-1}}. $$What does a larger standard deviation indicate?

Accepted Answer

Data values are more spread out from the mean.

Question 15

A data set has a mean of 50 and a standard deviation of 0. What does this tell you about the data?

Accepted Answer

All data values are equal to 50.

Question 16

Which of the following is TRUE about stem-and-leaf plots?

Accepted Answer

They preserve individual data values.

Question 17

A dotplot is most useful for which type of data?

Accepted Answer

Small quantitative data sets

Question 18

When describing a distribution, which three features should always be mentioned?

Accepted Answer

Shape, center, spread

Question 19

If a histogram has two distinct peaks, how would you describe its modality?

Accepted Answer

Bimodal

Question 20

Which of the following is the best summary of when to use mean and standard deviation versus median and IQR?

Accepted Answer

Use mean and standard deviation for symmetric distributions without outliers; use median and IQR for skewed distributions or those with outliers.

Displaying and Summarizing Data: Categorical and Quantitative Variables

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