Quartile Calculator

Enter numbers (separated by commas or spaces)

Import CSV/Excel File

First Quartile (Q1):

Second Quartile (Q2):

Third Quartile (Q3):

Interquartile Range (IQR):

Median:

x̃:

Minimum:

Maximum:

Range:

First Quartile (Q1)

The First Quartile (Q1) is the value below which the lowest 25% of the dataset lies. It represents the boundary between the lowest quarter and the rest of the data.

How to calculate:

Sort the dataset in ascending order.
Divide the dataset into two halves.
Find the median of the lower half (excluding the median if the dataset has an odd number of values).

Example:

Dataset: $2, 4, 6, 8, 10, 12, 14$

Lower half: $2, 4, 6$

Q1 = Median of $2, 4, 6$ = 4

Second Quartile (Q2)

The Second Quartile (Q2) is the median, dividing the dataset into two equal halves. It represents the 50th percentile.

How to calculate:

Sort the dataset in ascending order.
If the dataset has an odd number of values, the middle value is the median.
If it has an even number of values, the median is the average of the two middle values.

Example:

Dataset: $2, 4, 6, 8, 10, 12, 14$

Q2 = Median of the dataset = 8

Third Quartile (Q3)

The Third Quartile (Q3) is the value below which 75% of the data lies. It represents the boundary between the top 25% and the rest of the dataset.

How to calculate:

Sort the dataset in ascending order.
Divide the dataset into two halves.
Find the median of the upper half (excluding the median if the dataset has an odd number of values).

Example:

Dataset: $2, 4, 6, 8, 10, 12, 14$

Upper half: $10, 12, 14$

Q3 = Median of $10, 12, 14$ = 12

Interquartile Range (IQR)

The Interquartile Range (IQR) is the range of the middle 50% of the dataset, calculated as the difference between Q3 and Q1.

Formula:

IQR = Q_3 - Q_1

Example:

Q3 = 12, Q1 = 4

IQR = $12 - 4 = 8$

Median

The Median is the central value of a sorted dataset, dividing it into two equal halves.

x̃ (Mean)

The Mean, denoted by $\bar{x}$ , is the arithmetic average of the dataset.

Formula:

\bar{x} = \frac{\text{Sum of all values}}{\text{Number of values}}

Example:

Dataset: $2, 4, 6, 8, 10, 12, 14$

Mean = $\frac{2 + 4 + 6 + 8 + 10 + 12 + 14}{7} = 8$

Minimum

The Minimum is the smallest value in the dataset.

Example:

Dataset: $2, 4, 6, 8, 10, 12, 14$

Minimum = 2

Maximum

The Maximum is the largest value in the dataset.

Example:

Dataset: $2, 4, 6, 8, 10, 12, 14$

Maximum = 14

Range

The Range measures the difference between the maximum and minimum values.

Formula:

\text{Range} = \text{Maximum} - \text{Minimum}

Example:

Maximum = 14, Minimum = 2

Range = $14 - 2 = 12$