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Difficulty: EasyFrequency Distributions, Tables, and Grouped Data

The table below shows the frequency distribution of customer satisfaction ratings collected by a service center over a 50-day monitoring period.

Rating IntervalFrequency (Days)
1–58
6–1012
11–1520
16–2010

Based on the table, what percentage of the days had a customer satisfaction rating of 11 or higher?

  1. A
    20%
  2. B
    40%
  3. C
    50%
  4. 60%Answer
  5. E
    75%

Answer

60%
To find the percentage of days with a customer satisfaction rating of 11 or higher, add the frequencies of the intervals '11–15' (20 days) and '16–20' (10 days) to get 30 days. The total number of days across all intervals is 8 + 12 + 20 + 10 = 50 days. The percentage is (30 / 50) × 100% = 60%.

Step-by-Step Solution

1
Identify the relevant rating intervals.
The intervals corresponding to a rating of 11 or higher are '11–15' and '16–20'.
Ratings of 11 or higher include all data points within these two top intervals.
2
Sum the frequencies for the relevant intervals.
Frequency = 20 + 10 = 30 days.
Combining the frequencies gives the total number of favorable outcomes.
3
Calculate the total number of days across all intervals.
Total days = 8 + 12 + 20 + 10 = 50 days.
The total frequency represents the denominator for the percentage calculation.
4
Compute the percentage.
(30 / 50) × 100% = 60%.
Dividing the target frequency by the total frequency and multiplying by 100 yields the required percentage.

Key Concept

Frequency Table Percentages and Grouped Data Cutoffs
Estimated Time:45s
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Topics

Frequency Distributions, Tables, and Grouped Data

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