Histogram Analysis Worksheet
TEKS S(4)(C) Quantitative Data Analysis
Histogram Data Analysis
Name:
Date: Period:
Directions: Use the histograms below to evaluate frequencies, calculate subgroup totals, analyze distribution shapes, and determine threshold quantities.
1 Dataset A: English Test Score Distribution
Benchmark Model Question & Extensions
Grades on the English Test 40 30 20 10 0 Number of Students ~14 ~22 ~34 ~44 ~38 ~24 40 50 60 70 80 90 100 Grade on Test
1. (Same Type: At Least) Approximately how many students scored at least 70 on the test?
A. 202
B. 106
C. 93
D. 149
Show calculation:
2. (Different Type: Proportion) What is the total number of students who took the test, and what percentage scored below 60?
Total Students (\(N\)):
% Scoring Below 60:
2 Dataset B: Morning Commute Times (Minutes)
Threshold Queries & Cumulative Analysis
Daily Commute Duration 30 20 10 0 Number of Commuters 16 32 24 12 6 2 3 0 10 20 30 40 50 60 70 80 Commute Time (Minutes)
3. (At Most Threshold) How many commuters have a travel time of no more than 30 minutes?
A. 48
B. 72
C. 84
D. 95
Interval sum:
4. (Same Type: At Least) Approximately how many commuters have a travel time of at least 30 minutes?
A. 20
B. 23
C. 12
D. 47
Interval sum (include all bars \(\ge 30\)):
Key Strategy: "At least \(k\)": \(\ge k\) (sum all bars at & to the right) • "At most \(k\)": \(\le k\) (sum all bars at & to the left)
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Histogram Analysis Answer Key
TEACHER KEY TEKS S(4)(C) Scoring Guide & Solutions
Histogram Analysis Answer Key
Assessment Status Full Exemplar Key
Instructional Focus: Cumulative threshold calculations ("at least" / "at most"), relative frequencies, and outlier inclusion. Total: 4 Items • 10 Points
1 Dataset A: English Test Score Solutions
Benchmark Model & Extension
Frequencies
[40, 50): 14
[50, 60): 22
[60, 70): 34
[70, 80): 44
[80, 90): 38
[90, 100]: 24
Total (\(N\)): 176
1. At Least 70 on Test Correct: B (106)
Step: Sum bars \(\ge 70\): 44 (70–80) + 38 (80–90) + 24 (90–100) = 106 students.
*Common trap: Including the 60–70 interval (140) or only counting peak bar (44).
2. Total Population & Proportion Below 60
Total Students (\(N\)): 176 students (Accept 174–178)
% Scoring Below 60: ≈ 20.5% (or 20%) \(\frac{14 + 22}{176} = \frac{36}{176}\)
2 Dataset B: Commute Times Solutions
Paired Threshold Analysis
Frequencies
0–10 min: 16
10–20 min: 32
20–30 min: 24
30–40 min: 12
40–50 min: 6
50–60 min: 2
60–70 min: 0
70–80 min: 3 (outlier)
Total Commuters: 95
3. No More Than 30 Minutes (\(\le 30\)) Correct: B (72)
Step: Sum bars \(\le 30\): 16 (0–10) + 32 (10–20) + 24 (20–30) = 72 commuters.
*Common trap: Counting only 20–30 min (24) or adding 30–40 min.
4. At Least 30 Minutes (\(\ge 30\)) Correct: B (23)
Step: Sum all bars \(\ge 30\): 12 (30–40) + 6 (40–50) + 2 (50–60) + 0 + 3 (70–80) = 23 commuters.
*Common trap: Forgetting outlier bin 70–80 (getting 20, Choice A) or only counting 30–40 (12, Choice C). Notice complement: \(72 + 23 = 95\) total!
TEKS S(4)(C) Quick Scoring Guide (10 Points Total)
Q1 (2 pts): 1 pt work (bars 70–100); 1 pt answer 106 (Choice B).
Q2 (3 pts): 1 pt total \(N \approx 176\); 2 pts proportion \(\approx 20\%\).
Q3 (2 pts): 1 pt work (bars 0–30); 1 pt answer 72 (Choice B).
Q4 (3 pts): 2 pts summing all intervals \(\ge 30\) incl. outlier; 1 pt answer 23 (Choice B).
Histogram Distribution Analysis • Teacher Answer Key & Scoring Guide Page 1 of 1
