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Percentiles

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Topics

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

Meaning

  • Percentiles are values that divide a sorted data set into 100 equal parts.
  • There are 99 percentiles (P₁, P₂, ..., P₉₉), each marking a dividing point.
Maharashtra State Board: Class 11

Calculation

A. For Individual or Discrete Data 
Formula:
\[\mathrm{P}_k=\mathrm{size~of}k\left(\frac{n+1}{100}\right)^\text{th Observation}\] k = 1, 2,... 99

Where: 

  • k = Percentile number (1 to 99)
  • n = Total number of observations

B. For Grouped/Continuous Data 
Formula: 
\[\mathbf{P}_k=l+\left(\frac{\frac{kn}{100}-cf}{f}\right)\times h\]         k = 1, 2,... 99
Where
P = Percentile
l = Lower limit of percentile class
f = Frequency of percentile class
cf = Cumulative frequency of class preceding percentile class
h = Upper limit of the class – lower limit of the percentile class.

Maharashtra State Board: Class 11

Application

Percentiles are widely used to interpret test results, health indicators, income or wealth levels, and in comparing student scores or benchmarks across populations.

Maharashtra State Board: Class 11

Real-Life Application

Think of a school marathon: If a runner is at the 47th percentile, they ran faster than 47% of other runners.

Maharashtra State Board: Class 11

Key Point Summary

  • Percentiles are positional stats dividing data into 100 parts.
  • Calculation differs for individual/discrete and grouped/continuous data.
  • Used for comparing performance (tests, income, health, etc.). 

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