Math Problem Statement

Determine the IQR of the data below.

Determine the IQR of the data below.

Solution

The sorted data is: 8,10,11,13,14,14,14,14,16,17,178, 10, 11, 13, 14, 14, 14, 14, 16, 17, 17.

  • First Quartile (Q1): 12.0
  • Third Quartile (Q3): 15.0
  • Interquartile Range (IQR): 3.0

The IQR is the difference between Q3 and Q1, which is 3.0.

Would you like further details or have any questions?

Here are 5 related questions to expand on this topic:

  1. How is the interquartile range (IQR) useful in detecting outliers?
  2. How do you calculate quartiles when the data size is very large?
  3. What is the difference between IQR and standard deviation in measuring spread?
  4. Can you explain the significance of the median in relation to quartiles?
  5. How would adding or removing a number affect the IQR of this dataset?

Tip: The IQR is a robust measure of variability, as it is less sensitive to extreme values compared to the range.

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Math Problem Analysis

Mathematical Concepts

Statistics
Interquartile Range (IQR)
Quartiles

Formulas

IQR = Q3 - Q1

Theorems

Quartiles theorem
IQR theorem

Suitable Grade Level

Grades 7-10