Box Plot Comparison Review
TEKS S(4)(E) | Summary Statistics & Distributions
Test Prep Review
Target Standard: Compare and contrast meaningful information derived from summary statistics given a data set.
Name:
Date:
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Scenario: An electronics quality laboratory evaluated the continuous battery runtime (in hours) of two high-performance laptops during heavy 4K video rendering. Random samples from both models are summarized in the parallel box plots below. Use this data display to answer Questions 1–3.
VoltBook Pro (Hours) 5 6.5 10 13.5 15.5 TitanCore 15 (Hours) 9 11 12 13 14.5 4 6 8 10 12 14 16 BATTERY RUNTIME (HOURS)
Question 1
Which statements accurately describe the two box plots shown above?
I. The distribution for the TitanCore 15 data has a higher center.
II. The distribution for the TitanCore 15 data has a lower center.
III. The variation or spread for the distribution of the VoltBook Pro data is larger.
IV. The variation or spread for the distribution of the VoltBook Pro data is smaller.
A I and III
B II and III
C II and IV
D I and IV
Question 2
What is the difference between the interquartile range (IQR) of the VoltBook Pro and the IQR of the TitanCore 15?
VoltBook Pro IQR:
TitanCore 15 IQR:
A 1.5 hours
B 3.5 hours
C 5.0 hours
D 7.0 hours
Question 3
Based on the box plots, which statement correctly compares or interprets the 25th, 50th, or 75th percentiles of the distributions?
A The 25th percentile of the TitanCore 15 (11.0 hours) is greater than the 50th percentile of the VoltBook Pro (10.0 hours).
B The 25th percentile of the VoltBook Pro is 5.0 hours and its 75th percentile is 15.5 hours.
C The 50th percentile of the VoltBook Pro is greater than the 50th percentile of the TitanCore 15.
D Approximately 75% of the TitanCore 15 laptops had a battery runtime greater than its 75th percentile of 13.0 hours.
High School Statistics Review • Parallel Box Plot Distributions TEKS S(4)(E) Assessment
Box Plot Comparison Key
TEKS S(4)(E) | Teacher Answer Key & Explanations
Official Key
Resource: Box Plot Comparison Review • Distributions of Continuous Data (Laptop Battery Runtimes)
Question 1 Center & Spread
A
Question 2 Difference in IQR
C
Question 3 25th / 50th / 75th
A
Summary Statistics Master Reference Derived directly from parallel box plots
| Distribution | Min | \(Q_1\) (25th %) | Median (50th %) | \(Q_3\) (75th %) | Max | IQR (\(Q_3 - Q_1\)) | Range |
|---|
| VoltBook Pro | 5.0 | 6.5 | 10.0 hrs | 13.5 | 15.5 | 7.0 hrs | 10.5 hrs |
| TitanCore 15 | 9.0 | 11.0 | 12.0 hrs | 13.0 | 14.5 | 2.0 hrs | 5.5 hrs |
Q1 Explanation Correct Answer: A (Statements I and III)
- Statement I is TRUE: Center in a box plot is given by the median (the vertical bar inside the box). TitanCore 15 has a median of 12.0 hours, whereas VoltBook Pro has a median of 10.0 hours (\(12.0 > 10.0\)).
- Statement II is FALSE: Contradicts Statement I since TitanCore 15 has a higher center, not lower.
- Statement III is TRUE: Variation or spread is quantified by Range (\(\text{Max} - \text{Min}\)) and IQR (\(Q_3 - Q_1\)). VoltBook Pro has a Range of 10.5 hours vs. TitanCore's 5.5 hours, and an IQR of 7.0 hours vs. TitanCore's 2.0 hours. VoltBook's spread is significantly larger.
- Statement IV is FALSE: Contradicts Statement III.
Q2 Explanation Correct Answer: C (5.0 hours)
VoltBook Pro IQR = \(Q_3 - Q_1 = 13.5 - 6.5 = \mathbf{7.0\text{ hours}}\)
TitanCore 15 IQR = \(Q_3 - Q_1 = 13.0 - 11.0 = \mathbf{2.0\text{ hours}}\)
Difference = \(7.0 - 2.0 = \mathbf{5.0\text{ hours}}\)
Teaching Note: While students compute IQR without a provided formula, reinforce that the box width spans the middle 50% of values (\(Q_3 - Q_1\)).
Q3 Explanation Correct Answer: A (25th, 50th, & 75th Percentile Evaluation)
Why A is TRUE: The 25th percentile is the first quartile (\(Q_1\)), and the 50th percentile is the median. For TitanCore 15, \(Q_1 = \mathbf{11.0\text{ hours}}\). For VoltBook Pro, the median is \(\mathbf{10.0\text{ hours}}\). Because \(11.0 > 10.0\), at least 75% of the TitanCore 15 laptops lasted longer than the median runtime of the VoltBook Pro.
Why Distractors are Incorrect:
- B is false: 5.0 and 15.5 are the Minimum and Maximum of VoltBook Pro, not its 25th (\(6.5\)) and 75th (\(13.5\)) percentiles.
- C is false: VoltBook's 50th percentile is 10.0 hrs, which is less than TitanCore's 50th percentile of 12.0 hrs.
- D is false: At the 75th percentile (13.0 hrs), 75% of data is less than or equal to 13.0 hrs; only 25% exceeds it.
High School Statistics Review • Answer Key & Pedagogical Rationale TEKS S(4)(E) Teacher Resource
