Calculating and Interpreting IQR from Data Sets

Reviewed by Editorial Team
The ProProfs editorial team is comprised of experienced subject matter experts. They've collectively created over 10,000 quizzes and lessons, serving over 100 million users. Our team includes in-house content moderators and subject matter experts, as well as a global network of rigorously trained contributors. All adhere to our comprehensive editorial guidelines, ensuring the delivery of high-quality content.
Learn about Our Editorial Process
| By Thames
T
Thames
Community Contributor
Quizzes Created: 7116 | Total Attempts: 9,522,086
| Questions: 20 | Updated: Oct 31, 2025
Please wait...
Question 1 / 20
0 %
0/100
Score 0/100
1) What is the median of this data set?

Explanation

The middle value in the ordered list (11 numbers) is the 6th one. Counting to the 6th gives 10, so the median is 10.

Submit
Please wait...
About This Quiz
Calculating And Interpreting Iqr From Data Sets - Quiz

Ready to explore the interquartile range (IQR) and how it gives us insight into the spread of data? This quiz will guide you through calculating Q1, Q3, and the IQR for various data sets—whether it’s students’ reading habits, soccer player ages, or daily temperatures. You'll also dive into identifying outliers... see moreand interpreting the IQR to understand how data is spread and what that means for real-world scenarios. By the end, you’ll be equipped to calculate the IQR and interpret it in the context of data sets, helping you make informed decisions based on data distribution. Let's get started! see less

2)
We’ll put your name on your report, certificate, and leaderboard.
2) What is the median temperature?

Explanation

14 values. Median = average of 7th and 8th = (68 + 70)/2 = 69.

Submit
3) What is Q1 for the temperature data?

Explanation

Lower half: 58,60,62,63,65,67,68. Middle (4th) is 63. So Q1 = 63.

Submit
4) What is Q3 for the temperature data?

Explanation

Upper half: 70,72,73,75,78,80,85. Middle (4th) is 75. So Q3 = 75.

Submit
5) What is the IQR for the temperature data?

Explanation

IQR = Q3 − Q1 = 75 − 63 = 12.

Submit
6) To identify potential outliers using the IQR method, you calculate boundaries at Q1 − 1.5(IQR) and Q3 + 1.5(IQR). If Q1 = 20 and Q3 = 40, what is the upper boundary for outliers?

Explanation

IQR = 40 − 20 = 20. Upper boundary = Q3 + 1.5×IQR = 40 + 1.5×20 = 40 + 30 = 70.

Submit
7) A data set has Q1 = 12, Q3 = 28, and IQR = 16. What is the lower boundary for identifying outliers?

Explanation

Lower boundary = Q1 − 1.5×IQR = 12 − 1.5×16 = 12 − 24 = −12.

Submit
8) What is the first quartile (Q1) of this data set?

Explanation

Lower half: 3, 5, 7, 8, 9. The middle of these is 7, so Q1 = 7.

Submit
9) Using the IQR method, what is the upper boundary for outliers?

Explanation

Upper boundary = Q3 + 1.5×IQR = 28 + 1.5×13 = 28 + 19.5 = 47.5.

Submit
10) Is the score of 45 points an outlier?

Explanation

45 < 47.5. So 45 is not an outlier.

Submit
11) Two classes took the same math test. Class A has an IQR of 8 points, and Class B has an IQR of 22 points. What can you conclude?

Explanation

Smaller IQR means more consistent middle scores. Class A (IQR 8) is more consistent than Class B (IQR 22).

Submit
12) What is the third quartile (Q3) of this data set?

Explanation

Upper half: 12,14,15,16,22. Middle is 15. So Q3 = 15.

Submit
13) A data set showing monthly rainfall has Q1 = 2.5 inches, median = 3.8 inches, and Q3 = 5.1 inches. What is the IQR, and what does it represent?

Explanation

IQR = Q3 − Q1 = 5.1 − 2.5 = 2.6 inches. It shows the spread of the middle 50% of rainfall.

Submit
14) What is the interquartile range (IQR) for this data set?

Explanation

IQR = Q3 − Q1 = 15 − 7 = 8.

Submit
15) What is Q1 for the ages of soccer participants?

Explanation

Lower half (exclude median 9th): 6,7,7,8,8,9. Q1 = average of 3rd and 4th = (7 + 8)/2 = 7.5.

Submit
16) What is Q3 for the ages of soccer participants?

Explanation

Upper half: 9,10,10,11,12,13. Q3 = average of 3rd and 4th = (10 + 11)/2 = 10.5.

Submit
17) What is the IQR for the ages of soccer participants?

Explanation

IQR = Q3 − Q1 = 10.5 − 7.5 = 3.

Submit
18) What does the IQR of 3 years tell us about the ages in this soccer league?

Explanation

IQR of 3 means the middle 50% of ages span 3 years.

Submit
19)  A data set has Q1 = 15 and Q3 = 32. What is the IQR?

Explanation

IQR = Q3 − Q1 = 32 − 15 = 17.

Submit
20) The test scores for a class have Q1 = 68 and IQR = 18. What is Q3?

Explanation

Q3 = Q1 + IQR = 68 + 18 = 86.

Submit
View My Results
Cancel
  • All
    All (20)
  • Unanswered
    Unanswered ()
  • Answered
    Answered ()
What is the median of this data set?
What is the median temperature?
What is Q1 for the temperature data?
What is Q3 for the temperature data?
What is the IQR for the temperature data?
To identify potential outliers using the IQR method, you calculate...
A data set has Q1 = 12, Q3 = 28, and IQR = 16. What is the lower...
What is the first quartile (Q1) of this data set?
Using the IQR method, what is the upper boundary for outliers?
Is the score of 45 points an outlier?
Two classes took the same math test. Class A has an IQR of 8 points,...
What is the third quartile (Q3) of this data set?
A data set showing monthly rainfall has Q1 = 2.5 inches, median = 3.8...
What is the interquartile range (IQR) for this data set?
What is Q1 for the ages of soccer participants?
What is Q3 for the ages of soccer participants?
What is the IQR for the ages of soccer participants?
What does the IQR of 3 years tell us about the ages in this soccer...
 A data set has Q1 = 15 and Q3 = 32. What is the IQR?
The test scores for a class have Q1 = 68 and IQR = 18. What is Q3?
Alert!

Back to Top Back to top
Advertisement