Deciles are statistical measures that divide a dataset into ten equal parts, each containing an equal number of observations. They are a form of quantiles, which are points taken at regular intervals from the cumulative distribution function (CDF) of a dataset. By segmenting data into ten distinct groups, deciles provide a meaningful way to interpret and analyze data distribution.
Calculation of Deciles
To calculate deciles, the data must be sorted in ascending order. The decile thresholds are determined based on the following formula:
where \( D_i \) represents the i-th decile and \( N \) is the number of observations. The deciles are located at the 10th, 20th, 30th, up to the 90th percentiles of the ordered data.
Example Calculation
Consider the dataset: [3, 7, 8, 5, 12, 14, 21, 13, 18, 26]
-
Ordering the Data:
$$ 3, 5, 7, 8, 12, 13, 14, 18, 21, 26 $$ -
Decile Calculation:
- 1st Decile (10th percentile): 3 + 0.1 * (5 - 3) = 3.2
- 5th Decile (50th percentile or median): 13
- 9th Decile (90th percentile): 21 + 0.1 * (26 - 21) = 21.5
Types of Deciles
There are three primary types of deciles:
- Lower Deciles (1st to 3rd): Represent the lower end of the data distribution.
- Middle Deciles (4th to 7th): Encompass the central portion of the distribution.
- Upper Deciles (8th to 10th): Cover the higher end of the distribution.
Applicability of Deciles
Deciles are widely used in various fields, including:
- Economics and Finance: To measure income distribution, wealth quintiles, and economic disparities.
- Education: To categorize test scores and academic performance.
- Marketing: To segment customer data and target specific market groups.
Historical Context
The concept of deciles dates back to the development of percentiles in the early 20th century, as statisticians sought ways to summarize and interpret large datasets effectively. Deciles have since become a standard tool in descriptive statistics.
Comparisons and Related Terms
- Quartiles: Divide data into four equal parts.
- Percentiles: Divide data into 100 equal parts.
- Quintiles: Divide data into five equal parts.
- Tertiles: Divide data into three equal parts.
Related Definitions
Quartile: Each of the four equal groups into which a dataset can be divided.
Percentile: A measure indicating the value below which a given percentage of observations fall.
FAQs
How do deciles differ from percentiles?
Can deciles be used for non-numeric data?
References
- “Fundamentals of Statistics” by S.C. Gupta and V.K. Kapoor
- “Statistics for Business and Economics” by Paul Newbold, William L. Carlson, and Betty Thorne
Summary
Deciles are a valuable statistical tool for dividing a dataset into ten equal parts, making them essential for various analytical purposes. By providing insight into the distribution of data, deciles help in understanding economic conditions, educational outcomes, and market trends. For anyone dealing with large datasets, mastering the use of deciles can offer significant advantages.
