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 $9$ declles. They are denoted by the symbol $D_{1}, D_{2}, D_{3} D_{9} .$ 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 $P_{1}, P_{2}, P_{3}, \ldots P_{99}$.
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 $9$ declles. They are denoted by the symbol $D_{1}, D_{2}, D_{3} D_{9} .$ 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 $P_{1}, P_{2}, P_{3}, \ldots P_{99}$.
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