Finite Mathematics Quiz: Summarizing Data
5 questions · exam conditions
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Summarizing DataQuestion 1 of 5

A marketing team collected survey data on customer satisfaction ratings (1-5 scale) from 200 customers across three product categories. They want to create a summary table showing both the frequency distribution and relative frequency for each rating level. If Product A received ratings of: fifty 5's, forty 4's, thirty 3's, fifteen 2's, and five 1's, what should be the relative frequency (as a percentage) for ratings of 3 or higher?

85.7%
60.0%
75.0%
42.9%
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Finite Mathematics Quiz

Finite Mathematics Quiz: Summarizing Data

Practice Summarizing Data in Finite Mathematics with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Summarizing Data, giving you a quick way to practice the rules, question types, and explanations that matter most for Finite Mathematics.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A marketing team collected survey data on customer satisfaction ratings (1-5 scale) from 200 customers across three product categories. They want to create a summary table showing both the frequency distribution and relative frequency for each rating level. If Product A received ratings of: fifty 5's, forty 4's, thirty 3's, fifteen 2's, and five 1's, what should be the relative frequency (as a percentage) for ratings of 3 or higher?

  1. 85.7% (correct answer)
  2. 60.0%
  3. 75.0%
  4. 42.9%
Explanation: First, calculate total responses for Product A: 50+40+30+15+5 = 140. Ratings of 3 or higher: 50+40+30 = 120. Relative frequency = (120/140) × 100% = 85.7%. Choice B incorrectly uses 200 as denominator (120/200 = 60%). Choice C uses wrong numerator (105/140). Choice D only includes ratings 4 and 5 (90/140 = 64.3% rounded incorrectly).

Question 2

A retail chain manager is creating a performance summary table from sales data across 8 store locations. The monthly sales figures (in thousands) are: Store 1: $245K, Store 2: $189K, Store 3: $278K, Store 4: $156K, Store 5: $234K, Store 6: $298K, Store 7: $167K, Store 8: $203K. When organizing this data into quartiles for the summary report, which stores would be classified as 'Below Average Performers' if this category includes stores in the first quartile and any stores performing below the overall mean?

  1. Stores 2, 4, and 7, representing the bottom quartile of performance with significant improvement needs
  2. Stores 4 and 7 only, constituting the lowest quartile requiring immediate management attention
  3. Stores 2, 4, 7, and 8, including first quartile plus below-mean performers needing support (correct answer)
  4. Stores 4, 7, and 8, representing all locations falling below performance benchmarks
Explanation: First, sort the data: 156, 167, 189, 203, 234, 245, 278, 298. Q1 position = 2.25, so Q1 = 167 + 0.25(189-167) = 172.5. First quartile includes stores with sales ≤ 172.5K: Stores 4 (156K)and7(156K) and 7 (167K). Mean = (245+189+278+156+234+298+167+203)/8 = 221.25K. Below-mean stores: 4 (156K),7(156K), 7 (167K), 2 (189K),8(189K), 8 (203K). Combined: Stores 2, 4, 7, 8. Choice A misses Store 8. Choice B only includes Q1 stores. Choice D misses Store 2.

Question 3

A research team collected test scores from three different classes and wants to create a comparative summary table. Class A has scores: 85, 88, 92, 78, 95, 82, 90. Class B has scores: 75, 80, 85, 88, 82, 79, 84, 86. Class C has scores: 90, 94, 87, 91, 89, 93. When organizing these data into a summary table with measures of central tendency, which class shows the smallest difference between its mean and median values?

  1. Class A with a difference of 0.9 points, indicating nearly symmetric score distribution
  2. Class B with a difference of 0.6 points, showing balanced central tendency measures
  3. Class C with a difference of 0.2 points, demonstrating the most symmetric data distribution (correct answer)
  4. Class A with a difference of 1.2 points, reflecting moderate skewness in the dataset
Explanation: Class A: Mean = (85+88+92+78+95+82+90)/7 = 87.1, Median = 88, |Difference| = 0.9. Class B: Mean = (75+80+85+88+82+79+84+86)/8 = 82.4, Median = (82+84)/2 = 83, |Difference| = 0.6. Class C: Mean = (90+94+87+91+89+93)/6 = 90.7, Median = (90+91)/2 = 90.5, |Difference| = 0.2. Class C has the smallest difference at 0.2 points.

Question 4

A dataset of 20 observations is recorded: 53, 61, 64, 68, 70, 72, 72, 75, 76, 79, 81, 82, 82, 82, 85, 88, 90, 91, 95, 98.

A researcher creates a histogram for this data using a class width of 10, with the first class being [50,60)[50, 60). If the researcher then decides to re-summarize the data using a class width of 20, with the first class being [50,70)[50, 70), which of the following would be a direct consequence of this change?

  1. The total area of the bars in the histogram would be doubled to account for the wider bins.
  2. The new histogram would reveal more specific details about the distribution's central tendency.
  3. The shape of the distribution would change from roughly symmetric to distinctly skewed.
  4. The number of bars would be reduced, potentially obscuring features of the distribution. (correct answer)
Explanation: Increasing the class width (bin size) in a histogram reduces the number of classes (bars). The original histogram with width 10 would have classes [50, 60), [60, 70), [70, 80), [80, 90), [90, 100). The new histogram with width 20 would have classes [50, 70), [70, 90), [90, 110). This consolidation of data into fewer, wider bars results in a loss of detail and can obscure features like skewness or modality that might have been visible with smaller bins. The total area remains proportional to the total frequency, it does not double. Wider bins hide detail, they don't reveal it. The underlying distribution shape doesn't change, but its visual representation might, though not necessarily from symmetric to skewed in a predictable way.

Question 5

A university registrar is analyzing enrollment data to create summary statistics for department planning. The data shows credit hours attempted by students: 12 credits (45 students), 15 credits (120 students), 18 credits (85 students), 21 credits (35 students), and 24 credits (15 students). When preparing a weighted frequency table that accounts for total credit hour load rather than just student count, what is the modal credit hour category based on total credit hours generated?

  1. 15 credits, generating the highest total credit volume with 1,800 total credit hours (correct answer)
  2. 18 credits, producing maximum credit generation with 1,530 total hours across students
  3. 12 credits, creating the largest credit hour contribution at 540 total hours
  4. 21 credits, yielding peak credit hour production with 735 total credit hours
Explanation: Calculate total credit hours for each category: 12×45=540, 15×120=1,800, 18×85=1,530, 21×35=735, 24×15=360. The 15-credit category generates 1,800 total credit hours, which is the highest. This differs from the simple frequency mode (15 credits based on student count) but represents the modal category when weighted by credit hour production. Choice B has correct calculation but wrong conclusion. Choices C and D show correct individual calculations but miss the comparison.