Middle School Math Quiz: Interpreting Box Plots
4 questions · exam conditions
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Interpreting Box PlotsQuestion 1 of 4

Two schools compare their students' performance on a standardized test using box plots. School A has Q1 = 520, median = 580, Q3 = 640. School B has Q1 = 540, median = 580, Q3 = 620. An administrator concludes that "both schools performed equally well since they have the same median." Which analysis of this conclusion is most appropriate?

The conclusion is valid because the median is the best single measure for comparing test performance between schools
The conclusion is incomplete because School B shows more consistent performance with a smaller IQR of 80 compared to School A's IQR of 120
The conclusion is incorrect because School A has a wider range of scores, indicating more students at both high and low performance levels
The conclusion is reasonable because both schools have 50% of students scoring 580 or above, showing similar achievement levels
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Middle School Math Quiz

Middle School Math Quiz: Interpreting Box Plots

Practice Interpreting Box Plots in Middle School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Interpreting Box Plots, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Two schools compare their students' performance on a standardized test using box plots. School A has Q1 = 520, median = 580, Q3 = 640. School B has Q1 = 540, median = 580, Q3 = 620. An administrator concludes that "both schools performed equally well since they have the same median." Which analysis of this conclusion is most appropriate?

  1. The conclusion is valid because the median is the best single measure for comparing test performance between schools
  2. The conclusion is incomplete because School B shows more consistent performance with a smaller IQR of 80 compared to School A's IQR of 120 (correct answer)
  3. The conclusion is incorrect because School A has a wider range of scores, indicating more students at both high and low performance levels
  4. The conclusion is reasonable because both schools have 50% of students scoring 580 or above, showing similar achievement levels
Explanation: School A IQR = 640 - 520 = 120. School B IQR = 620 - 540 = 80. While both have the same median, School B shows more consistent performance with less variability in the middle 50% of scores. The conclusion is incomplete because it ignores the consistency aspect. Choice A overstates the median's importance. Choice C mentions range but focuses on extremes rather than the relevant IQR comparison. Choice D restates what equal medians mean without addressing the consistency difference.

Question 2

A researcher creates a box plot from survey data about daily screen time (in hours) for teenagers. The box plot shows Q1 = 4, median = 6, Q3 = 8, with whiskers extending to 2 and 11 hours. If the researcher wants to identify teenagers with "unusually high" screen time using the 1.5 × IQR rule, what is the minimum number of hours of daily screen time that would be considered unusually high?

  1. Any screen time greater than 8 hours should be considered unusually high
  2. Any screen time greater than 11 hours should be considered unusually high
  3. Any screen time greater than 14 hours should be considered unusually high (correct answer)
  4. Any screen time greater than 17 hours should be considered unusually high
Explanation: Using the 1.5 × IQR rule: IQR = Q3 - Q1 = 8 - 4 = 4 hours. The upper fence = Q3 + 1.5(IQR) = 8 + 1.5(4) = 8 + 6 = 14 hours. Any value above 14 hours is considered unusually high (an outlier). Choice A uses Q3, choice B uses the maximum whisker value, and choice D incorrectly calculates the fence.

Question 3

Two box plots compare marathon completion times (in hours) for runners in different age groups. The younger group has Q1 = 3.2, median = 3.8, Q3 = 4.5. The older group has Q1 = 3.6, median = 4.2, Q3 = 4.8. If both groups have the same number of runners, which comparison of their performances is most justified?

  1. The older group performed better because their times are more consistent, with a smaller IQR of 1.2 hours compared to 1.3 hours
  2. The younger group performed better because their median time is faster and their IQR shows similar consistency at 1.3 hours (correct answer)
  3. The groups performed equally well because both have an IQR of 1.3 hours, indicating identical variability in performance
  4. The younger group performed better because 75% finished faster than the older group's median time of 4.2 hours
Explanation: Younger group IQR = 4.5 - 3.2 = 1.3 hours. Older group IQR = 4.8 - 3.6 = 1.2 hours. The younger group has a faster median (3.8 vs 4.2 hours) and nearly the same consistency (IQR of 1.3 vs 1.2). Choice A incorrectly calculates the younger group's IQR. Choice C states both IQRs are 1.3. Choice D is incorrect because Q3 for younger group is 4.5, meaning only 75% finished by 4.5 hours, not 4.2 hours.

Question 4

A box plot displays the heights (in inches) of basketball players on a team. The plot shows that Q1 = 70 inches and Q3 = 76 inches. A coach states that "the team has good height consistency since most players are within 6 inches of each other." Evaluate the accuracy of the coach's reasoning.

  1. The coach's reasoning is correct because the IQR of 6 inches shows that 75% of players are within this range
  2. The coach's reasoning is incorrect because the IQR of 6 inches represents only 50% of players, not most of the team (correct answer)
  3. The coach's reasoning is correct because an IQR of 6 inches indicates low variability for basketball player heights
  4. The coach's reasoning is incomplete because we need the full range from minimum to maximum to assess consistency
Explanation: IQR = Q3 - Q1 = 76 - 70 = 6 inches, but this represents the range containing the middle 50% of players, not 'most' of the team. The coach incorrectly interprets what the IQR represents. Choice A incorrectly states the IQR covers 75%. Choice C makes a judgment about what constitutes 'low variability' without context. Choice D misses the main error in the coach's reasoning about what percentage the IQR represents.