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Quartile Calculator

Input your dataset values, separated by commas or spaces, click the 'Calculate' button, and analyze the data distribution.

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Quartile Calculator:

This Quartile calculator calculates the quartiles (Q1, Q2, Q3) of a dataset and provides key statistics and visual representation to help understand data distribution. It also provides:

Median
Minimum and Maximum values
Interquartile Range (IQR)
Count (Total Numbers)
Average
Geometric Mean

What Are Quartiles?

Quartiles divide a dataset into four equal parts. The three quartiles (Q1, Q2, Q3) create four intervals, each containing roughly 25% of the data points.

Q1 – Lower Quartile: The 25th percentile of the data; 25% of values fall below Q1 and 75% above it.

Q2 – Median Quartile: The median of the dataset; 50% of values fall below and 50% above.

Q3 – Upper Quartile: The 75th percentile; 75% of values fall below Q3 and 25% above it.

Interquartile Range (IQR): Measures the spread of the middle 50% of the dataset: $$ IQR = Q3 - Q1 $$

Use the IQR calculator for instant calculations.

quartile

How to Calculate Quartiles?

Step 1: Order the Dataset

Arrange all data points in ascending order.

Step 2: Count the Data Points

Determine the total number of data points (n). If n is odd, the middle value is the median. If n is even, calculate the mean of the two central values.

Step 3: Find Q2 (The Median)

Q2 is the median, dividing the dataset into two equal halves.

Step 4: Determine Q1 (First Quartile)

Q1 is the median of the lower half of the dataset. If n is odd, exclude Q2.

Step 5: Find Q3 (Third Quartile)

Q3 is the median of the upper half of the dataset. If n is odd, exclude Q2.

How to Find the Interquartile Range (IQR)?

$$ IQR = Q3 - Q1 $$

Example:

Dataset: 2, 7, 9, 11, 13, 23, 16

Step 1: Order the data

2, 7, 9, 11, 13, 16, 23

Step 2: Total number of terms

n = 7

Step 3: Find Q1

Position: $$ Q1 = (n+1) \times \frac{1}{4} = 2 $$

Q1 = 2nd value = 7

Step 4: Find Q2

Position: $$ Q2 = (n+1) \times \frac{2}{4} = 4 $$

Q2 = 4th value = 11

Step 5: Find Q3

Position: $$ Q3 = (n+1) \times \frac{3}{4} = 6 $$

Q3 = 6th value = 16

Step 6: Calculate IQR

$$ IQR = Q3 - Q1 = 16 - 7 = 9 $$

Use the online quartile calculator to quickly determine quartiles and visualize the IQR.

Why Do We Calculate Quartiles?

Analyzing Data Distribution: Understand how data is spread around mean or median.
Identifying Outliers: Detect extreme values outside the typical range.
Calculating IQR: Measure spread of the middle 50%.
Comparing Datasets: Evaluate similarities and differences.
Generating Box Plots: Visualize data distribution.
Decision Making: Support trends analysis and risk assessment.

For quick calculations, use our statistics quartile calculator.

Difference Between Lower and Third Quartile

The difference between Q3 and Q1 is the IQR, which measures the spread of the middle 50%:

$$ IQR = Q3 - Q1 $$

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