# Empirical relationship between measures of dispersion

### Measures of Dispersion I

What is the relationship between of mean, median, mode, and standard deviation ? All three are measures of central tendency or averages that have their. The range is the difference between the largest and the smallest observation in the data. The prime advantage of this measure of dispersion is that it is easy to. Chebyshev's Theorem and The Empirical rule. Chebyshev's A measure of statistical dispersion is a nonnegative real number that is zero if all the data .. Pearson's correlation coefficient between two variables is defined as the covariance of.

Only when the range is "narrow" meaning that there are no outliers does it tell us about typical values in the data. Percentiles and related characteristics Most students are familiar with the grading scale in which "C" is assigned to average scores, "B" to above-average scores, and so forth.

### Relationship Between Measures Of Dispersion Assignment Help

When grading exams "on a curve," instructors look to see how a particular score compares to the other scores. The letter grade given to an exam score is determined not by its relationship to just the high and low scores, but by its relative position among all the scores. Percentile describes the relative location of points anywhere along the range of a distribution. A score that is at a certain percentile falls even with or above that percent of scores.

The median score of a distribution is at the 50th percentile: Commonly used percentile measures are named in terms of how they divide distributions. Quartile Finder Find the quartile scores for the following distribution. See instructions appearing below the histogram.

The divisions you have just performed illustrate quartile scores. In theory, percentile scores divide a distribution into equal sized groups. In practice this may not be possible because the number of cases may be under A box plot is an effective visual representation of both central tendency and dispersion.

It simultaneously shows the 25th, 50th medianand 75th percentile scores, along with the minimum and maximum scores.

The length of the whiskers indicate visually how extreme the outliers are. Below is the box plot for the distribution you just separated into quartiles. The boundaries of the box plot's "box" line up with the columns for the quartile scores on the histogram.

## Measures of dispersion

The box plot displays the median score and shows the range of the distribution as well. Variance and Standard Deviation By far the most commonly used measures of dispersion in the social sciences are variance and standard deviation.

**Measures of Dispersion part-1**

Variance is the average squared difference of scores from the mean score of a distribution. It should be capable of further algebraic treatment. It should have sampling stability. It should not be unduly affected by the extreme items.

Absolute measures of dispersion are expressed in the same units in which the original data are expressed. For example, if the series is expressed as Marks of the students in a particular subject; the absolute dispersion will provide the value in Marks.

The only difficulty is that if two or more series are expressed in different units, the series cannot be compared on the basis of dispersion. The basic advantage of this measure is that two or more series can be compared with each other despite the fact they are expressed in different units. But from a practical point of view, relative or coefficient of dispersion is considered better as it is used to make comparison between series.

### Measures of dispersion

Methods of Dispersion Methods of studying dispersion are divided into two types: In this category, commonly used measures of dispersion are: Where we want to study only the extent of variation, whether it is higher or lesser a Lorenz-curve is used. Mathematical Methods a Range It is the simplest method of studying dispersion. Range is the difference between the smallest value and the largest value of a series.