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Quartiles and percentiles are statistical measures that divide a dataset into groups or sections based on their position or rank within the dataset. Quartiles divide the dataset into four equal parts, while percentiles divide it into 100 equal parts. These measures are commonly used in data analysis to understand the distribution and variability of data. By calculating quartiles and percentiles, we can determine the range, spread, and central tendency of a dataset, making it easier to compare and interpret data. They are especially useful in identifying outliers and understanding the overall shape of a dataset. These statistical measures are widely used in various fields, such as finance, economics, and social sciences, to analyze and interpret data accurately.
Statistics – Quartiles and Percentiles
Quartiles and percentiles are measures of variation, which describes how spread out the data is.
Quartiles and percentiles are both types of quantiles.
Quartiles
Quartiles are values that separate the data into four equal parts.
Here is a histogram of the age of all 934 Nobel Prize winners up to the year 2020, showing the quartiles:
The quartiles (Q0,Q1,Q2,Q3,Q4) are the values that separate each quarter.
Between Q0 and Q1 are the 25% lowest values in the data. Between Q1 and Q2 are the next 25%. And so on.
- Q0 is the smallest value in the data.
- Q1 is the value separating the first quarter from the second quarter of the data.
- Q2 is the middle value (median), separating the bottom from the top half.
- Q3 is the value separating the third quarter from the fourth quarter
- Q4 is the largest value in the data.
Calculating Quartiles with Programming
Quartiles can easily be found with many programming languages.
Using software and programming to calculate statistics is more common for bigger sets of data, as finding it manually becomes difficult.
Example
With Python use the NumPy library quantile() method to find the quartiles of the values 13, 21, 21, 40, 42, 48, 55, 72:
import numpy values = [13,21,21,40,42,48,55,72]
x = numpy.quantile(values, [0,0.25,0.5,0.75,1])
print(x)
Example
Use the R quantile() function to find the quantiles of the values 13, 21, 21, 40, 42, 48, 55, 72:
values <- c(13,21,21,40,42,48,55,72) quantile(values)
Percentiles
Percentiles are values that separate the data into 100 equal parts.
For example, The 95th percentile separates the lowest 95% of the values from the top 5%
The 25th percentile (P25%) is the same as the first quartile (Q1).
The 50th percentile (P50%) is the same as the second quartile (Q2) and the median.
The 75th percentile (P75%) is the same as the third quartile (Q3)
Calculating Percentiles with Programming
Percentiles can easily be found with many programming languages.
Using software and programming to calculate statistics is more common for bigger sets of data, as finding it manually becomes difficult.
Example
With Python use the NumPy library percentile() method to find the 65th percentile of the values 13, 21, 21, 40, 42, 48, 55, 72:
import numpy values = [13,21,21,40,42,48,55,72]
x = numpy.percentile(values, 65)
print(x)
Example
Use the R quantile() function to find the 65th percentile (0.65) of the values 13, 21, 21, 40, 42, 48, 55, 72:
values <- c(13,21,21,40,42,48,55,72) quantile(values, 0.65)
Cite this article
stats writer (2024). What are the statistics behind quartiles and percentiles?. PSYCHOLOGICAL SCALES. Retrieved from https://scales.arabpsychology.com/stats/what-are-the-statistics-behind-quartiles-and-percentiles/
stats writer. "What are the statistics behind quartiles and percentiles?." PSYCHOLOGICAL SCALES, 29 Jun. 2024, https://scales.arabpsychology.com/stats/what-are-the-statistics-behind-quartiles-and-percentiles/.
stats writer. "What are the statistics behind quartiles and percentiles?." PSYCHOLOGICAL SCALES, 2024. https://scales.arabpsychology.com/stats/what-are-the-statistics-behind-quartiles-and-percentiles/.
stats writer (2024) 'What are the statistics behind quartiles and percentiles?', PSYCHOLOGICAL SCALES. Available at: https://scales.arabpsychology.com/stats/what-are-the-statistics-behind-quartiles-and-percentiles/.
[1] stats writer, "What are the statistics behind quartiles and percentiles?," PSYCHOLOGICAL SCALES, vol. X, no. Y, ص Z-Z, June, 2024.
stats writer. What are the statistics behind quartiles and percentiles?. PSYCHOLOGICAL SCALES. 2024;vol(issue):pages.