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This quartile calculator and interquartile range calculator finds first quartile Q₁, second quartile Q₂ and third quartile Q₃ of a data set. It also finds median, minimum, maximum, and interquartile range.

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Quartiles

Quartiles mark each 25% of a set of data:

• The first quartile Q₁ is the 25th percentile
• The second quartile Q₂ is the 50th percentile
• The third quartile Q₃ is the 75th percentile

The second quartile Q₂ is easy to find. It is the median of any data set and it divides an ordered data set into upper and lower halves.

The first quartile Q₁ is the median of the lower half not including the value of Q₂. The third quartile Q₃ is the median of the upper half not including the value of Q₂.

How to Calculate Quartiles

1. Order your data set from lowest to highest values
2. Find the median. This is the second quartile Q₂.
3. At Q₂ split the ordered data set into two halves.
4. The lower quartile Q₁ is the median of the lower half of the data.
5. The upper quartile Q₃ is the median of the upper half of the data.

If the size of the data set is odd, do not include the median when finding the first and third quartiles.

If the size of the data set is even, the median is the average of the middle 2 values in the data set. Add those 2 values, and then divide by 2. The median splits the data set into lower and upper halves and is the value of the second quartile Q₂.

How to Find Interquartile Range

The interquartile range IQR is the range in values from the first quartile Q₁ to the third quartile Q₃. Find the IQR by subtracting Q₁ from Q₃.

• IQR = Q₃ - Q₁

How to Find the Minimum

The minimum is the smallest value in a sample data set.

Ordering a data set from lowest to highest value, x₁ ≤ x₂ ≤ x₃ ≤ ... ≤ x_n, the minimum is the smallest value x₁. The formula for minimum is:

\[ \text{Min} = x_1 = \text{min}(x_i)_{i=1}^{n} \]

How to Find the Maximum

The maximum is the largest value in a sample data set.

Ordering a data set from lowest to highest value, x₁ ≤ x₂ ≤ x₃ ≤ ... ≤ x_n, the maximum is the largest value x_n. The formula for maximum is:

\[ \text{Max} = x_n = \text{max}(x_i)_{i=1}^{n} \]

How to Find the Range of a Set of Data

The range of a data set is the difference between the minimum and maximum. To find the range, calculate x_n minus x₁.

\[ R = x_n - x_1 \]

 

References

[1] Wikipedia contributors. "Quartile." Wikipedia, The Free Encyclopedia. Last visited 10 April, 2020.