Q: Suppose you want to construct a relative frequency distribution for the Yelp ratings. Which formula should you use to calculate the relative frequency for each rating?

$$\text{Relative Frequency} = \frac{\text{Frequency of a rating}}{\text{Total number of ratings}}$$

Question 1

Which of the following best describes the variable 'Yelp rating' as shown in the bar graph for Hot Doug’s Restaurant?

Accepted Answer

Quantitative and discrete, because ratings are countable whole numbers.

Question 2

In the bar graph for Hot Doug’s Yelp ratings, what are the most appropriate labels for the x-axis and y-axis?

Accepted Answer

x-axis: Yelp Star Rating; y-axis: Number of Ratings

Question 3

Which level of measurement is represented by the Yelp star ratings (1-5 stars) for Hot Doug’s Restaurant?

Accepted Answer

Ordinal

Question 4

Suppose the Yelp ratings for Hot Doug’s are: 1 star (35), 2 stars (67), 3 stars (246), 4 stars (724), 5 stars (1675). What is the mode of this distribution?

Accepted Answer

5 stars

Question 5

Based on the Yelp ratings bar graph, which statement best describes the shape of the distribution?

Accepted Answer

Skewed left (negatively skewed)

Question 6

The second image shows dollar signs of different sizes to represent percentages. Why might this graph be considered misleading?

Accepted Answer

The area (not just height) of the dollar signs exaggerates differences between categories.

Question 7

Which of the following would improve the accuracy of the 'Most Popular Ways to Save for College' graph?

Accepted Answer

Use a bar graph with bars proportional in height to the percentages.

Question 8

If a survey about college savings was conducted only among parents attending a financial seminar, which type of bias is most likely present?

Accepted Answer

Sampling bias

Question 9

A researcher wants to compare the average Yelp rating for Hot Doug’s to the average for all restaurants in the city. Which of the following is a parameter?

Accepted Answer

The average rating for all Yelp reviews of Hot Doug’s.

Question 10

If the mean Yelp rating for Hot Doug’s is pulled down by a few very low ratings, which measure of central tendency would best represent a typical rating?

Accepted Answer

Median

Question 11

Suppose you want to construct a relative frequency distribution for the Yelp ratings. Which formula should you use to calculate the relative frequency for each rating?

Accepted Answer

$$	ext{Relative Frequency} = \frac{	ext{Frequency of a rating}}{	ext{Total number of ratings}}$$

Question 12

If the 'Most Popular Ways to Save for College' survey used a convenience sample, what is a likely consequence?

Accepted Answer

The results may not be representative of the population.

Question 13

Which sampling method would be most appropriate to ensure all types of college savers are represented in the survey?

Accepted Answer

Stratified sampling

Question 14

If the mean, median, and mode of Yelp ratings for Hot Doug’s are all approximately equal, what does this suggest about the distribution?

Accepted Answer

The distribution is symmetric and unimodal.

Question 15

A survey finds that 37% of respondents use a savings account to save for college. This value is a:

Accepted Answer

Statistic, because it describes a sample.

Question 16

If the minimum Yelp rating is 1 and the maximum is 5, and you want to create 5 classes for a frequency distribution, what is the class width?

Accepted Answer

$$	ext{Class width} = \frac{5-1}{5} = 0.8$$, round up to 1

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