Analyzing IQR and Data Distribution

Grade 9th

Reviewed by Cierra Henderson

Cierra Henderson, MBA |

K-12 Expert

Review Board Member

Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.

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By Thames

Thames

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Quizzes Created: 11121 | Total Attempts: 9,743,875

| Questions: 20 | Updated: Jan 22, 2026

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1) Which class likely has a larger IQR?

Class X

Class Y

They are the same

IQR cannot be estimated

Class X has scores from 62 to 88, and Class Y has scores from 50 to 98. Given that Class Y has a wider range, it is likely to have a larger IQR.

Explanation

Class X has scores from 62 to 88, and Class Y has scores from 50 to 98. Given that Class Y has a wider range, it is likely to have a larger IQR.

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About This Quiz

Analyzing Iqr and Data Distribution - Quiz

Get ready to dive deep into the Interquartile Range (IQR) and discover how it can reveal insights about data distribution. This quiz will help you compare data sets, understand how to interpret the spread, and assess the consistency of various scenarios. You'll learn how to use box plots, IQRs, and... see moreother statistical measures to make comparisons, and analyze variability in data. Whether it’s student performance, sports team times, or delivery services, you’ll learn how the IQR is a powerful tool for interpreting data consistency and spread. Let’s see what you’ve got!
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2)

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2) If the IQR for Service B is approximately 20 minutes and for Service A is approximately 8 minutes, what does this tell you about variability?

Service A has greater variability

Service B has greater variability

Both have equal variability

IQR does not measure variability

Since Service A has a smaller IQR (8), it has less variability compared to Service B (20).

Explanation

Since Service A has a smaller IQR (8), it has less variability compared to Service B (20).

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3) If a manager wants more predictable delivery timing, which service should they prefer?

Service B, because larger IQR means more variety

Service B, because it has faster minimum

Either service; IQR is unrelated to predictability

Service A, because smaller IQR means more consistent middle times

Since Service A has a smaller IQR, it is more predictable.

Explanation

Since Service A has a smaller IQR, it is more predictable.

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4) Which service has the smaller IQR?

Service B

Service A

They are the same

Cannot be determined

For Service A: The data set is: 22, 24, 25, 26, 27, 28, 30, 31, 33, 33, 34, 35. For Service B: The data set is: 15, 18, 20, 22, 25, 27, 35, 38, 40, 42, 45, 50. The IQR for Service A is smaller (approximately 8) compared to Service B (approximately 20).

Explanation

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5) If both have the same median but different IQRs, what does that imply?

Centers differ but spreads are equal

Centers are equal but spreads differ

Both centers and spreads differ

Neither center nor spread can be compared

Since the medians are the same but the IQRs differ, it means that the centers are equal but the spreads (variability) differ.

Explanation

Since the medians are the same but the IQRs differ, it means that the centers are equal but the spreads (variability) differ.

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6) Which statement is the best comparison of consistency between M and N?

M is more consistent than N

N is more consistent than M

Both have equal consistency

Consistency cannot be inferred from IQR

Since Data Set M has a smaller IQR (6) compared to Data Set N (30), M is more consistent.

Explanation

Since Data Set M has a smaller IQR (6) compared to Data Set N (30), M is more consistent.

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7) Which has the larger IQR?

Both equal

Cannot determine

For Data Set M: The box is narrow (Q1 ≈ 42, Q3 ≈ 48), so the IQR is 48 - 42 = 6. For Data Set N: The box is wide (Q1 ≈ 30, Q3 ≈ 60), so the IQR is 60 - 30 = 30. Thus, Data Set N has the larger IQR.

Explanation

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8) If the principal wants the class with the tightest middle 50% of scores for a pilot program, which should be chosen?

Class Y

Class X

Either class, since IQRs are equal

Neither class

Class X has a smaller IQR, meaning the middle 50% of its scores are tighter.

Explanation

Class X has a smaller IQR, meaning the middle 50% of its scores are tighter.

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9) Which class demonstrates greater consistency in scores?

Class Y, because higher scores mean consistent

Both, because both have 12 scores

Class Y, because larger IQR

Class X, because smaller IQR

A smaller IQR indicates greater consistency. Since Class X has a smaller IQR (13), it demonstrates greater consistency.

Explanation

A smaller IQR indicates greater consistency. Since Class X has a smaller IQR (13), it demonstrates greater consistency.

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10) If Class X’s IQR is about 13 and Class Y’s IQR is about 25, which is true?

Class Y has more variability

Class X has more variability

Both have equal variability

IQR shows center, not spread

The IQR reflects the spread of the middle 50% of data. Since Class Y has a larger IQR (25), it has more variability.

Explanation

The IQR reflects the spread of the middle 50% of data. Since Class Y has a larger IQR (25), it has more variability.

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11) Which subject has the larger IQR?

Math

They have the same IQR

English

Not enough information

We first need to find the IQRs for both subjects: For Math: Q1 ≈ 25, Q3 ≈ 35. IQR = 35 - 25 = 10. For English: Q1 ≈ 18, Q3 ≈ 40. IQR = 40 - 18 = 22. Thus, English has the larger IQR.

Explanation

We first need to find the IQRs for both subjects: For Math: Q1 ≈ 25, Q3 ≈ 35. IQR = 35 - 25 = 10. For English: Q1 ≈ 18, Q3 ≈ 40. IQR = 40 - 18 = 22. Thus, English has the larger IQR.

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12) A box plot shows Team B’s box is much wider and slightly higher median than Team A. Which is the best conclusion?

Team B is faster and more consistent

Team B is more variable and has a slightly higher center

Team A is more variable and has a higher center

Team A is slower and more consistent

Since Team B has a wider box (indicating a larger IQR), it is more variable. A higher median also suggests that Team B is faster on average.

Explanation

Since Team B has a wider box (indicating a larger IQR), it is more variable. A higher median also suggests that Team B is faster on average.

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13) If Team A’s Q1 and Q3 are approximately 11.3 and 12.1, and Team B’s Q1 and Q3 are approximately 11.0 and 13.0, what is true?

Team A IQR ≈ 0.8; Team B IQR ≈ 2.0; Team B more variable

Team A IQR ≈ 2.0; Team B IQR ≈ 0.8; Team A more variable

Both IQRs ≈ 1.0; equal variability

IQR compares center not spread

Team A IQR = 12.1 - 11.3 = 0.8. Team B IQR = 13.0 - 11.0 = 2.0. Since Team B has a larger IQR, it is more variable.

Explanation

Team A IQR = 12.1 - 11.3 = 0.8. Team B IQR = 13.0 - 11.0 = 2.0. Since Team B has a larger IQR, it is more variable.

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14) Which team shows more consistent sprint performance?

Team B

Both are equally consistent

Consistency cannot be assessed with IQR

Team A

Consistency is determined by the IQR. A smaller IQR indicates more consistency. Since Team A has a smaller range of times, it shows more consistent sprint performance.

Explanation

Consistency is determined by the IQR. A smaller IQR indicates more consistency. Since Team A has a smaller range of times, it shows more consistent sprint performance.

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15) Which team likely has the larger IQR?

Team A

Team B

They are equal

Not enough data

For Team A: the times are clustered between 11.0 and 12.4, showing less variation. For Team B: the times range from 10.7 to 13.5, showing more variation. Thus, Team B is likely to have the larger IQR.

Explanation

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16) If the teacher wants the subject with more predictable nightly time, which should they choose?

Math, because its IQR is smaller

English, because its IQR is smaller

English, because it has higher values

Either, because IQR doesn’t reflect predictability

Predictability is associated with consistency, which is shown by the IQR. A smaller IQR means more predictable times. Since Math has a smaller IQR (10), it is more predictable.

Explanation

Predictability is associated with consistency, which is shown by the IQR. A smaller IQR means more predictable times. Since Math has a smaller IQR (10), it is more predictable.

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17) Which statement best interprets the IQR for English in context?

Half of English homework times are within about 10 minutes

All English homework times are within the IQR

Half of English homework times are within about 21 minutes

The IQR indicates the mean time per day

The IQR for English is the difference between Q3 (40) and Q1 (18), which is 22 minutes. This means the middle 50% of English homework times fall within 22 minutes.

Explanation

The IQR for English is the difference between Q3 (40) and Q1 (18), which is 22 minutes. This means the middle 50% of English homework times fall within 22 minutes.

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18) If a box plot for Math is shorter than the box plot for English, what does this indicate?

Math has a larger IQR

They have the same spread

There are outliers in Math

English has a larger IQR

If a box plot for Math is shorter than the one for English, this means Math has a smaller IQR, implying English has a larger IQR.

Explanation

If a box plot for Math is shorter than the one for English, this means Math has a smaller IQR, implying English has a larger IQR.

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19) If Q1 and Q3 for Math are approximately 25 and 35, and for English are approximately 18 and 40, which statement is true?

Math IQR is larger, so Math is more variable

English IQR is larger, so English is more variable

Both IQRs are equal, so variability is the same

IQR only shows center, not spread

Math IQR = 35 - 25 = 10. English IQR = 40 - 18 = 22. Since the IQR for English is larger, English is more variable.

Explanation

Math IQR = 35 - 25 = 10. English IQR = 40 - 18 = 22. Since the IQR for English is larger, English is more variable.

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20) Which subject shows greater consistency in homework time?

Math

English

Both are equally consistent

Consistency cannot be determined

Consistency is related to the IQR. The subject with the smaller IQR shows more consistency. Since Math has a smaller IQR (10) compared to English's IQR (22), Math shows greater consistency.

Explanation

Consistency is related to the IQR. The subject with the smaller IQR shows more consistency. Since Math has a smaller IQR (10) compared to English's IQR (22), Math shows greater consistency.

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