# Quartiles, Quintiles, Deciles, and Percentile

## Quartiles

Quartiles divide a dataset into four equal parts, each containing 25% of the data. The first quartile (Q1) represents the 25th percentile, the second quartile (Q2) is the median, and the third quartile (Q3) corresponds to the 75th percentile.

These measures are useful in understanding the spread and central tendency of the data. For example, consider a dataset of exam scores: 60, 65, 70, 75, 80, 85, 90, 95. The first quartile (Q1) in this case would be 70, indicating that 25% of the students scored 70 or below. The second quartile (Q2) is the median, which is 80 in this example. Lastly, the third quartile (Q3) is 90, signifying that 25% of the students scored 90 or above.

## Quintiles

Quintiles are similar to quartiles but divide the data into five equal parts, with each part containing 20% of the data. The first quintile (Q1) represents the 20th percentile, the second quintile (Q2) is the 40th percentile, and so on, until the fifth quintile (Q5) represents the 100th percentile.

For instance, let's consider a dataset of monthly incomes: \$2,000, \$3,000, \$4,000, \$5,000, \$6,000, \$7,000, \$8,000, \$9,000. The first quintile (Q1) would be \$4,000, indicating that 20% of the individuals earn \$4,000 or less per month. The second quintile (Q2) is \$6,000, representing the 40th percentile, and so on.

## Deciles and Percentiles

Deciles and percentiles are further divisions of data, with deciles dividing it into ten equal parts and percentiles dividing it into one hundred equal parts. These measures provide more granularity in understanding the distribution of data.

For example, let's consider a dataset of house prices: \$100,000, \$150,000, \$200,000, \$250,000, \$300,000, \$350,000, \$400,000, \$450,000, \$500,000.

The first decile (D1) would be \$200,000, indicating that 10% of the houses are priced at \$200,000 or below.

The first percentile (P1) would be \$100,000, representing the 1st percentile, and so on. In conclusion, quartiles, quintiles, deciles, and percentiles are valuable statistical measures that help us understand the distribution of data and identify specific points within that distribution.

By dividing data into equal parts, these measures provide insights into the spread and central tendency of the data. Understanding these measures is crucial for making informed decisions and drawing meaningful conclusions from datasets.