Digital SATMath: Problem-Solving and Data AnalysisMedium
A health clinic collected data on the number of patients seen per day for a month. The data is summarized in a histogram. If the clinic saw between 10-19 patients on 5 days, 20-29 patients on 12 days, 30-39 patients on 8 days, and 40-49 patients on 5 days, what is the relative frequency of days where the clinic saw 30 or more patients?
- A0.33
- B0.43
- C0.16
- D0.25
Show answer & explanationAnswer & explanation
Correct answer: B. 0.43
Total number of days = 5 + 12 + 8 + 5 = 30 days. Number of days with 30 or more patients = 8 (for 30-39) + 5 (for 40-49) = 13 days. Relative frequency = 13 / 30 ≈ 0.433.
Why the other options are wrong
- A. This is 10/30 (approx 0.33), which might be a miscalculation of total days or target days.
- C. This is 5/30, which is the relative frequency of 10-19 or 40-49 patients, not 30 or more.
- D. This might be 8/30 or 5/20 if total days are miscalculated, or 12/30 (0.4) is wrong. (8/32 = 0.25)
Relative Frequency
Relative frequency is the proportion or fraction of times an event occurs in a dataset, calculated by dividing the frequency of the specific event by the total number of observations.
- Expressed as a decimal, fraction, or percentage.
- Sum of all relative frequencies for all categories is 1 (or 100%).
- Used to understand the distribution of data.
Memory trick: Part over Whole, always a fraction of the total.