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Deciles

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Topics

  • Meaning
  • Calculation
  • Application 
  • Real-Life Application
  • Key Point Summary
Maharashtra State Board: Class 11

Meaning

Deciles are points that divide a sorted data set into ten equal parts. There are nine decile values: D1 to D9. Each decile marks where 10%, 20%, ..., 90% of the data falls below that point.

Maharashtra State Board: Class 11

Calculation

1. For Individual or Discrete Data:
\[\mathrm{D}_j=j\left(\frac{n+1}{10}\right)^\text{th Observation}\mathrm{~where~}j=1,2...9\]

2. For Grouped (Continuous) Data:
\[\mathbf{D}_j=l+\left(\frac{\frac{jn}{10}-cf}{f}\right)\times h,\quad j=1,2...9\]
Where
D = Decile
l = Lower limit of decile class
f = Frequency of decile class
cf = Cumulative frequency of class preceding decile class
h = Upper limit of the class – lower limit of the decile class.

Maharashtra State Board: Class 11

Application

Deciles too have wide application in finance and economics. Government uses deciles to study the level of economic inequality, measurement of poverty line, drought conditions, etc. Deciles are used in investments, particularly to assess the performance of a portfolio investment such as a group of mutual funds. 

Maharashtra State Board: Class 11

Real-Life Application

  • Income Distribution: Government divides population into income deciles to study poverty or affluence.
  • Investments: Mutual funds classified into deciles by performance.
  • Academics: Exam scores grouped into deciles for rankings.
Maharashtra State Board: Class 11

Key Point Summary

  • Deciles split data into ten helpful sections for analysis.
  • Used to identify ranks, inequalities, or performance brackets.
  • Use the correct formula based on data type (individual vs. grouped). 

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