What are quartiles, deciles and percentiles in statistics?

A quartile is a statistical measure that divides a distribution into four equal parts. A quintile divides a distribution into five equal parts. A decile divides a distribution into ten equal parts. A percentile divides a distribution into one hundred equal parts. In this post, “what are quartiles, deciles, and percentiles in statistics?”, we will explain the concepts in simple terms. We will describe the methods of calculation of partition values: Quartiles, Deciles & Percentiles.

A distribution is simply a collection of data, or scores, on a variable. Usually, these scores are arranged in order from smallest to largest and then they can be presented graphically.

Page 6, Statistics in Plain English, Third Edition, 2010.

Usually, partition values are those values of the variable which divide the distribution into
a certain number of equal parts.

Here, please note that we should arrange data in ascending or descending order of magnitude.

As a matter of fact, commonly used partition values are quartiles, deciles, and percentiles.

For example, quartiles divide the data into four equal parts. Similarly, deciles and percentiles divide
the distribution into ten and hundred equal parts, respectively.

Quartiles

Quartiles divide the whole distribution into four equal parts.

Put another way, 1st Quartile contains the ¼ part of data, 2nd Quartile contains ½ of the data and 3rd Quartile contains the ¾ part of data. Repeating, it may be noted that the data should be arranged in
ascending or descending order of magnitude.

Deciles

In similar fashion, Deciles divide the whole distribution into ten equal parts.

Let’s discuss more. Deciles: 1st Decile, 2nd Decile,…,9th Decile and ith Decile contains the (iN/10)th part of data.

Here, please note that we should arrange data in ascending or descending order of magnitude.

Percentiles

In similar fashion, Percentiles divide the whole distribution into 100 equal parts.

Put another way, P1, P2, …, P99 are known as 1st percentile, 2nd percentile,…,99th percentile, and ith percentile contains the (iN/100)th part of data.

Here, please note that we should arrange data in ascending or descending order of magnitude.

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Frequently Asked Questions

What are quartiles and deciles?

Quartiles and deciles are statistical concepts that are commonly used to analyze datasets. Quartiles divide a dataset into four equal parts, with the first quartile (Q1) representing the 25th percentile, the second quartile (Q2) representing the median or 50th percentile, and the third quartile (Q3) representing the 75th percentile. On the other hand, deciles divide a dataset into ten equal parts, with the first decile (D1) representing the 10th percentile, the second decile (D2) representing the 20th percentile, and so on, until the tenth decile (D10) which represents the maximum value of the data.

What are quartiles deciles and percentiles called?

The terms “quartiles”, “deciles”, and “percentiles” collectively refer to statistical measures known as “quantiles”. Quantiles are used to divide a dataset into smaller equal parts or groups. Quartiles, deciles, and percentiles are all types of quantiles, with quartiles dividing a dataset into four equal parts, deciles dividing it into ten equal parts, and percentiles dividing it into one hundred equal parts. Therefore, these measures are all considered to be different types of quantiles.

What is Q1 Q2 Q3 and percentile?

Quartiles Q1, Q2 (median), and Q3 are statistical measures that split a dataset into four equal parts. Specifically, Q1 represents the value below which 25% of the data falls, Q2 represents the midpoint value that splits the data into the lower and upper halves, and Q3 represents the value below which 75% of the data falls. Percentile is another statistical measure that divides a dataset into 100 equal parts, with each percentile representing the percentage of data below that point.

What is decile formula?

Decile Value = (n + 1) x d / 10
Where “n” is the total number of values in the dataset, and “d” is the desired decile (for example, the fifth decile would be represented as “d = 5”). To apply the formula, you need to first order the dataset from smallest to largest, then find the position of the value that corresponds to the desired decile using the formula above. Finally, the corresponding value in the dataset for that position is the value of the specific decile.

The decile formula is used to calculate the value of a specific decile for a dataset. The formula involves finding the position of the value in the ordered dataset and then calculating the decile value based on that position.

What is the quartile formula?

The formula for finding Q1 and Q3 using the Tukey method is:
Q1 = Median of the lower half of the data set = (n+1)/4th observation if n is odd, where n is the sample size = Average of (n/4)th and (n/4 + 1)th observation if n is even
Q3 = Median of the upper half of the data set = (3n+1)/4th observation if n is odd = Average of (3n/4)th and (3n/4 + 1)th observation if n is even
where n is the sample size, and observations are sorted in ascending order.

Conclusion

To sum up, quartiles, deciles, and percentiles serve as important tools to measure the spread of data and provide insights into its distribution. They are frequently utilized in data analysis and offer valuable information on the relative positions of individual values within a given dataset.

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