Question
Explain the positional averages briefly.

Answer

  • If the observations of the data are not distributed around the average, then mean is not good. representative measure of observations of the data.
  • In this circumstances to know the characteristic of the data at various places.
considering the observations related to particular place of the data, the measure of average is obtained.
  • Such measure of average is known as the positional average.
  • Median is such a positional average. Besides this Quartiles, Deciles and Percentiles are also the measures of the positional average.
Median :
  • The value of observation dividing the observations of the data arranged in ascending or descending order of magnitudes Into two equal parts is called median of the data.
  • It is denoted by M. It represent the average value of 50% of observations.
Quartiles :
  • The values of observations dividing the sequence of observations of a given data arranged in the increasing or decreasing order of their magnitudes.
  • into four equal parts are called Quartiles.
  • There are three Quartiles and they are symbolically denoted as $Q_1, Q_2$ and $Q_3$.
Deciles :
  • The values of observations dividing the observations of a given data arranged in Increasing or decreasing order of their magnitudes in ten equal parts are called Deciles.
  • There are $9$ deciles. They are denoted by the symbol $D_1, D_2, D_3 \ldots \ldots D_9$.
Percentiles :
  • The values of observations dividing, the observations of a given data arranged in increasing, or decreasing order of their magnitudes in hundred equal parts are called Percentiles.
  • There are $99$ Percentiles. They are denoted by symbol $\mathrm{P}_1, \mathrm{P}_2, \mathrm{P}_3, \ldots . . \mathrm{P}_{99}$.

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