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Use this statistical tool to calculate the quartiles (q1, q2, & q3) for the data set.

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Quartile calculator is a tool that helps to find the quartiles of the data set values. You just need to enter the set of values separated by a comma or space and let this calculator find statistical values to understand how data is distributed:

- Lower Quartile (Q1)
- Median Quartile (Q2)
- Upper Quartile (Q3)
- Interquartile range (IQR)
- Average
- Geometric mean
- Total sum
- Population standard deviation
- Sample standard deviation
- Range
- Count (Total numbers)
- Graph to represent Quartiles

Quartiles are the statistical values that divide the dataset into four equal parts. There are three quartiles (Q1, Q2, and Q3) that create a four interval. Each of them contains roughly 25% of the data points.

**Q1 – Lower Quartile:**

Lower quartile (Q1) shows the 25th percentile of the data set. This means that 75% of the data points fall above it. This quartile separates the group with a ratio of 1:3

**Q2 – Median Quartile**

The median quartile means that the data is divided in half with 50% falling below and 50% falling above. Quartile Q2 is a point that splits the group with a ratio of 2:2

**Q3 – Upper Quartile**

The upper quartile means the 75% percentile of the given dataset. It means 75% of data falls below Q3 and the remaining 25% falls above it. This point separates the group into 3:1

**Interquartile Range (IQR)**

IQR is the analysis to determine how the values are spread in the middle 50 % of a dataset. It is the difference between the Q3 and the Q1. This can also be calculated with the help of an IQR Calculator.

These are formulas that help for calculating quartiles yourself:

Lower Quartile = \(\ Q1 = (n + 1) \times{\frac {1}{4}}\)

Median Quartile = \(\ Q2 = (n + 1) \times{\frac {2}{4}}\)

Upper Quartile = \(\ Q3 = (n + 1) \times{\frac {3}{4}}\)

Interquartile Range = \(\ IQR = Q3 - Q1\)

- Order your data set from least to greatest value
- Calculate the number of data points (n)
- Find Q2 that splits the given data set into two halves
- Q1 is the middle value of the lower half of the data set
- Q3 is the middle value of the upper half of the data set

Let us show these calculations with the example:

For the given set of data 2, 7, 9, 11, 13, 23, and 16 find the quartiles and interquartile range.

**Step 1: Order the data**

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

**Step 2: Calculate the total number of terms n**

Total terms (n) = 7

Here's how to find the positions of the quartiles:

**Step 3: Lower Quartile**

\(\ Q1 = (n + 1) \times{\frac {1}{4}}\)

\(\ Q1 = (7 + 1) \times{\frac {1}{4}}\) \(\ Q1 = 2\)

In the given data set the second value is 7

**Step 4: Median Quartile**

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

\(\ Q2 = (7 + 1) \times{\frac {2}{4}}\)

\(\ Q2 = 4\)

In the given data set the fourth value is 11

**Step 5: Upper Quartile**

\(\ Q3 = (n + 1) \times{\frac {3}{4}}\)

\(\ Q3 = (7 + 1) \times{\frac {3}{4}}\)

\(\ Q3 = 6\)

In the given data set the sixth value is 16

**Interquartile Range (IQR)**

\(\ IQR = Q3 - Q1\) \(\ IQR = 16 - 7\)

\(\ IQR = 9\)

You can also put the same values in the quartile calculator to find quartiles and how the IQR represents the range that contains the middle 50% of the data points.

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