Measures of Relative Position for
Grouped
Introduction:
There are measures of positions that are used to locate the relative position of a
specific data value about the rest of the data. The most popular measures of position
are:
1.) Standard scores it is also known as the z-scores
2.) Quantiles- this is divided into three such as
2.1 Quartiles(Q) - this is divided into three equal parts
2.2 Deciles(D) - this is divided into ten equal parts
2.3. Percentiles(P) - this is divided into 100 equal parts
Let us start with the z- scores:
Standard scores:
These are most commonly called z-scores; the two terms may be used interchangeably.
It is also called z-values, normal scores, and standardized variables.
To be able to compute a z-score this requires knowing the mean and standard deviation
of the complete population to which a data point belongs.
Mathematically speaking these are the formula for finding the z-scores:
1. If the population mean and population standard deviation are given :
2. If the sample mean, and sample standard deviation are given:
, Let us try the example;
A student scored 65 in a Calculus test with a mean score of 50 and a standard
deviation of 10. She then scored 30 in a History test with a mean score of 25 and a
standard deviation of 5. Compare her relative positions in the two courses.
Solution:
Let us proceed with the next measures of position.
The formula to be used will be the formula in finding the median.
Let us then recall the formula for finding the median of grouped data.
Using this formula we will be able to formulate the formula in finding the Quantiles.
Let's say for Quartile, we all know that this is divided into 4 equal parts, hence the
formula will have 4 as the denominator.
For Deciles instead of using four(4) as the denominator of n, we will use 10 as its
denominator
For Percentiles, the denominator will be 100.
Percentiles:
As we all know percentiles are divided into 100 equal parts hence each set of
observations has 99 percentiles and are denoted by P1,P2,...P99P1,P2,...P99
The formula to be used will be based on the median formula.
We will try to formulate the formula for each observation;
Grouped
Introduction:
There are measures of positions that are used to locate the relative position of a
specific data value about the rest of the data. The most popular measures of position
are:
1.) Standard scores it is also known as the z-scores
2.) Quantiles- this is divided into three such as
2.1 Quartiles(Q) - this is divided into three equal parts
2.2 Deciles(D) - this is divided into ten equal parts
2.3. Percentiles(P) - this is divided into 100 equal parts
Let us start with the z- scores:
Standard scores:
These are most commonly called z-scores; the two terms may be used interchangeably.
It is also called z-values, normal scores, and standardized variables.
To be able to compute a z-score this requires knowing the mean and standard deviation
of the complete population to which a data point belongs.
Mathematically speaking these are the formula for finding the z-scores:
1. If the population mean and population standard deviation are given :
2. If the sample mean, and sample standard deviation are given:
, Let us try the example;
A student scored 65 in a Calculus test with a mean score of 50 and a standard
deviation of 10. She then scored 30 in a History test with a mean score of 25 and a
standard deviation of 5. Compare her relative positions in the two courses.
Solution:
Let us proceed with the next measures of position.
The formula to be used will be the formula in finding the median.
Let us then recall the formula for finding the median of grouped data.
Using this formula we will be able to formulate the formula in finding the Quantiles.
Let's say for Quartile, we all know that this is divided into 4 equal parts, hence the
formula will have 4 as the denominator.
For Deciles instead of using four(4) as the denominator of n, we will use 10 as its
denominator
For Percentiles, the denominator will be 100.
Percentiles:
As we all know percentiles are divided into 100 equal parts hence each set of
observations has 99 percentiles and are denoted by P1,P2,...P99P1,P2,...P99
The formula to be used will be based on the median formula.
We will try to formulate the formula for each observation;
