Question

customers who buy an adventure game sold by an app store can give the game a rating from 1 star to 5 stars. the frequency table shows the number of 1 - star, 2 - star, 3 - star, 4 - star, and 5 - star ratings.
a. the game has a total of ___ ratings.
b. make a dot plot of the data set shown in the frequency table.
c. describe the shape and variability of the distribution.
d. how would the shape and variability of the distribution change if the game receives 20 more ratings of 5 stars?

Explanation:

Step1: Calculate the total number of ratings

Count the number of tally marks for each star - rating:

• For 1 - star: \(8\) (since a group of \(5\) and \(3\) more: \(5 + 3=8\))
• For 2 - star: \(4\)
• For 3 - star: \(1\)
• For 4 - star: \(3\)
• For 5 - star: \(7\) (a group of \(5\) and \(2\) more: \(5+2 = 7\))

Sum them up: \(8 + 4+1 + 3+7\)

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Step2: Analyze the shape and variability of the original distribution

• Shape: The distribution is skewed. There are more lower - star ratings (1 - star and 2 - star have relatively high frequencies compared to 3 - star, 4 - star, and 5 - star).
• Variability: There is a spread from 1 - star to 5 - star. The frequencies vary, with 1 - star being the most frequent (\(8\)) and 3 - star being the least frequent (\(1\))

Step3: Analyze the change when 20 more 5 - star ratings are added

• Shape: The distribution will become less skewed or even approximately symmetric (if we assume the new frequencies make the left and right sides more balanced). The peak will shift towards 5 - star.
• Variability: The spread is still from 1 - star to 5 - star. But the variability (measured in terms of how the data is distributed) will change. Since the frequency of 5 - star is increased significantly, the data will be more concentrated towards the higher end (5 - star)

Answer:

a. \(27\)
b. (To make a dot - plot: Draw a number line from \(1\) to \(5\). For 1 - star, place \(8\) dots; for 2 - star, place \(4\) dots; for 3 - star, place \(1\) dot; for 4 - star, place \(3\) dots; for 5 - star, place \(7\) dots)
c. Shape: Skewed (towards lower stars). Variability: Data is spread from 1 - star to 5 - star with different frequencies.
d. Shape: Less skewed (or more symmetric). Variability: Data will be more concentrated towards 5 - star (but still spread from 1 - star to 5 - star)