Relative Frequency Histogram Review
TEKS S(4)(C) • Quantitative Data Distributions
Statistics & Data Analysis Review
Name:
Date: Period:
1
A sports physiologist recorded the resting heart rate of a representative group of high school track athletes. The graph below displays a relative-frequency histogram for their resting heart rates (in beats per minute, bpm). Approximately what percentage of these athletes had a resting heart rate between 60 and 89 bpm inclusive?
Resting Heart Rates of Track Athletes Relative Frequency Resting Heart Rate (bpm) 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.12 0.34 0.28 0.18 0.08 50 60 70 80 90 100
A 62%
B 80%
C 46%
D 92%
Show Your Work & Mathematical Reasoning
Teacher Solution & Analysis Key
Relative Frequency Histogram Review
Correct Answer: B (80%)
Step-by-Step Solution
Step 1: Identify the Target Bins / Intervals
The question asks for the percentage of athletes with resting heart rates between 60 and 89 bpm inclusive. In standard histogram interval notation, this corresponds to three consecutive bins:
- Bin 1: \([60, 70)\)
- Bin 2: \([70, 80)\)
- Bin 3: \([80, 90)\)
Step 2: Read Relative Frequencies from the Histogram
Extract the vertical bar height (relative frequency) for each corresponding interval:
60–70 bpm 0.34
70–80 bpm 0.28
80–90 bpm 0.18
Step 3: Sum Relative Frequencies and Convert to Percentage
Add the relative frequencies together and multiply by \(100\%\):
$$\text{Total Relative Frequency} = 0.34 + 0.28 + 0.18 = 0.80$$ $$\text{Percentage} = 0.80 \times 100\% = 80\%$$
Distractor & Error Analysis
A (62%)
Omitted the 80–89 bpm bin, only adding \(0.34 + 0.28 = 0.62\).
C (46%)
Added only the first two bins \(0.12 + 0.34 = 0.46\) or only middle bins.
D (92%)
Included the lower 50–59 bpm bin (\(0.12 + 0.34 + 0.28 + 0.18 = 0.92\)).
Key Conceptual Reminder for Students
Relative frequency represents the proportion of the total dataset in each bin (\(\text{relative frequency} = \frac{\text{frequency}}{n}\)). The sum of all relative frequencies in a complete distribution equals \(1.00\) (\(100\%\)).
