Question 1

What is the Interquartile Range (IQR)?

Accepted Answer

The Interquartile Range (IQR) is a measure of statistical dispersion, representing the spread of the middle 50% of a dataset. It's calculated as IQR = Q3 - Q1, where Q1 is the first quartile (25th percentile) and Q3 is the third quartile (75th percentile). Unlike range, IQR is not affected by extreme values or outliers.

Question 2

How do you calculate the interquartile range?

Accepted Answer

To calculate IQR: 1) Arrange data in ascending order. 2) Find Q1 (median of lower half). 3) Find Q2 (median). 4) Find Q3 (median of upper half). 5) Calculate IQR = Q3 - Q1. For example, with data 1,3,5,7,9,11,13,15: Q1=5, Median=8, Q3=11, so IQR = 11-5 = 6.

Question 3

What are quartiles and the five-number summary?

Accepted Answer

Quartiles divide data into four equal parts: Q1 (25th percentile), Q2/Median (50th percentile), Q3 (75th percentile). The five-number summary consists of: Minimum, Q1, Median, Q3, Maximum. These five values completely describe the distribution and are used to create box plots.

Question 4

Why is IQR better than range for measuring spread?

Accepted Answer

IQR is more robust than range because it measures the spread of the middle 50% of data, ignoring outliers. Range (Max - Min) is heavily influenced by extreme values. For data with outliers, IQR provides a more representative measure of typical variability, making it preferred in exploratory data analysis.

Question 5

How do you identify outliers using IQR?

Accepted Answer

Outliers are identified using the 1.5×IQR rule: Lower bound = Q1 - 1.5×IQR, Upper bound = Q3 + 1.5×IQR. Values outside these bounds are considered outliers. For severe outliers, use 3×IQR rule. This method is part of the box plot construction and is widely used in statistical analysis.

Question 6

What is the difference between IQR and standard deviation?

Accepted Answer

IQR is a measure of spread that uses quartiles and is not affected by outliers. Standard deviation measures average distance from the mean and is sensitive to outliers. IQR is non-parametric (doesn't assume normal distribution), while standard deviation is parametric. IQR is best for skewed distributions, while SD is better for normal distributions.

Question 7

How do you calculate quartiles for grouped data?

Accepted Answer

For grouped data: 1) Calculate cumulative frequencies. 2) Find the group containing the quartile position. 3) Use linear interpolation within that group. Q1 is at 25% of data (position n/4), Q2 at 50% (n/2), Q3 at 75% (3n/4). Interpolation formula accounts for the interval width and frequency distribution.

Question 8

When do you use IQR in data analysis?

Accepted Answer

IQR is used in: comparative analysis of distributions, identifying outliers and anomalies, creating box plots, robust statistical measures, exploratory data analysis, quality control, and when data has outliers or is skewed. It's especially useful for non-normal distributions where standard deviation may be misleading.

Question 9

What does a large or small IQR indicate?

Accepted Answer

A large IQR indicates high variability in the middle 50% of data - values are spread out from each other. A small IQR indicates low variability - values cluster together. Comparing IQRs between groups reveals relative spread. Zero IQR means all middle values are identical (all equal to median).

Question 10

How is IQR used in box plots?

Accepted Answer

IQR defines the box in a box plot (whisker plot). The box spans from Q1 to Q3 (IQR height), with a line at median. Whiskers extend to minimum/maximum or 1.5×IQR bounds. Points beyond whiskers are outliers. Box plots visually show the five-number summary, making IQR essential for understanding distribution shape and spread.

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