Dispersion Meaning
You are free to use this image on your website, templates, etc, Please provide us with an attribution linkArticle Link to be Hyperlinked One can use dispersion to understand the variation in the values of the data set. It helps to assess the data quality in a quantifiable manner. In finance, it enables investors to determine the statistical distribution of probable returns on their investments. Range, variance, mean deviation, and standard deviation are some of the common measures of dispersion.
Dispersion in Statistics ExplainedDispersion (scatter or variation) can have multiple meanings based on the context it is used in. For instance, in statistics, it is the factor that helps determine the extent of variation of values in a particular data set. At the same time, it allows investors to estimate the statistical distribution of potential portfolio returnsThe portfolio return formula calculates the return of the total portfolio consisting of the different individual assets. The formula is computed by calculating the return on investment on individual asset multiplied with respective weight class in the total portfolio and adding all the resultants together. Rp = ∑ni=1 wi riread more in finance. Thus, spread is the measurement of the variability of an item from other items in a data set and from its central value. Usually, using the measure of central tendencCentral Tendency is a statistical measure that displays the centre point of the entire Data Distribution & you can find it using 3 different measures, i.e., Mean, Median, & Mode.read morey to describe a certain set of data is not enough. The measure of central tendency can help know the mean, median, or mode of data sets, but the measure of the variation can only be known through dispersion. Hence, the analysis of data using statistics is done by:
Measuring spread gives us accurate information on vertical data distribution statistics as per the histogram. However, the information obtained from it is more related to the separation of data points, the difference in the values of the data set, and the distance of every single data point from the mean value of the entire data set. In other words, it shows how data are spread and how different they are from one another, i.e., the homogeneity or heterogeneity of data in a distribution. If the distance between a data point and its mean value is:
You are free to use this image on your website, templates, etc, Please provide us with an attribution linkArticle Link to be Hyperlinked Measures of Dispersion in StatisticsThere are two methods to measure the degree of variation present in the data set:
#1 – Absolute MeasureIt refers to the average of deviations of data like standard deviation or mean deviation. It has the same unit assigned to the original data set like centimeters, meters, kilograms, etc. Here are some absolute measures of spread. You are free to use this image on your website, templates, etc, Please provide us with an
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Range refers to the difference between the largest and the smallest values in a given data set. The higher the value of the range, the higher the spread in data. R = L – D where, L = Largest value S = Smallest value
A quartile distributes a data set in four equal valued sets. Each data set has the smallest number, the largest number, and the median. Q2 or second quartile is the median of the data. The first quartile (Q1) connects the smallest number with Q2, while the third quartile (Q3) joins the largest number with Q2. The interquartile range is the difference between the third quartile and the first quartile. Half of the interquartile range is the quartile deviation. Hence, Interquartile range (IR) = Q3 – Q1
Mean deviation measures the deviation of data from its central point (mean, median, or mode). It is the arithmetic meanArithmetic mean denotes the average of all the observations of a data series. It is the aggregate of all the values in a data set divided by the total count of the observations.read more of the absolute deviations of the data from the central value. Mean deviation = Total of all absolute deviations value/ Total number of observations
It is the average of the sum of the square of the difference between each data point from the mean. The higher the variance, the higher the scattering of data from the mean and vice-versa. Σ = sum of, Χ = each value, μ = mean, Ν = number of values in the dataset
It is the most widely used method for measuring spread. Mathematically, it is the square root of the variance. where, #2 – Relative MeasureThe relative measure is a type of dispersion expressed in ratios and percentages. Since it is independent of original units, it is used for comparative analysis of two or more data set distributions with different units of measurement. Also, relative measures are used to compare datasets that have varying averages. You are free to use this image on your website, templates, etc,
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It is the ratio of the difference between the largest and smallest values in a distribution to the sum of the largest and smallest values in a distribution. COR = L-S/L+S where, L= largest value S = Smallest value
It is used to contrast two data sets based on their consistency. where, X = Mean σ = standard deviation
It is the standard deviation divided by the mean of the data set. COS = SD/Mean where, SD is the standard deviation
It is the ratio of the difference between the third and the first quartile to the sum of the third and the first quartile of the data set. COQ = Q3 – Q1/ Q3 + Q1
It is calculated using either the mean, median, or mode of the data. COM = MD/Mean Or COM = MD/Median Or COM = MD/Mode where, MD = Mean deviation ExamplesLet us go through the following dispersion examples for a better understanding of the concept. Example #1Let us take an example from the stock marketStock Market works on the basic principle of matching supply and demand through an auction process where investors are willing to pay a certain amount for an asset, and they are willing to sell off something they have at a specific price.read more domain. A certain security A is being traded on the exchange. The traders who want to invest in security A will look at its historical return data for the last year. They will assess the extent of scattering of the security’s return over the past year. If the degree of scattering of returns is less, it means less price fluctuation. Thus, the security will be considered a safer investment with low riskLow-risk investments are the financial instruments with minimal uncertainties or chances of loss to the investors. Although such investments are safe, they fail to offer high returns to the investors. read more. Moreover, if the degree of spread of security A is higher, it means the price is highly volatile. Therefore, the security will be taken as an unsafe investment in such a case. In other words, higher dispersion means riskier investment and vice versa. Example #2Let’s consider two varieties of coffee – X & Y with different yields. Coffee X and Y have the following yields for a period of six months:
To know the spread of each variety of coffee, let’s calculate its range. Range (R) = Largest value (L) – Smallest Value (S)
As mentioned before, the higher the range, the greater the data spread. Thus,
Therefore, X has a lower spread than Y. Lower spread means better yield, and a higher spread represents lower yield. Hence, higher dispersion in data means lesser returns, and lower dispersion in the data set means higher returns. Frequently Asked QuestionsWhat does dispersion mean in statistics? Dispersion means the scale of distribution of data around a central point or value. It shows the distance of values in a distribution from the central value. It plays an important role in gauging the volatility, quality, and yield of data sets under statistical observation. What causes dispersion? Dispersion of data happens in statistics because of natural phenomena, irregular behavior of observational data, and due to technical errors of data measuring instruments. All these factors contribute to the dispersion of data in statistics. What are the three measures of dispersion? Dispersion is measured in absolute or relative terms. The most commonly used measures of spread are range, variance, and standard deviation. Range is the difference between the highest and lowest value in a distribution. Variance is derived by adding the square of the difference between each value in the distribution and the mean and then, dividing it by the number of values in a data set. Standard deviation is the square root of variance. Recommended ArticlesThis has been a guide to Dispersion in Statistics & its Meaning. Here we discuss the measures of dispersion of data in a distribution, along with examples. You can learn more about accounting from the following articles –
What term describe the amount of spread dispersion or variability of the item in a distribution?Standard deviation (SD) is the most commonly used measure of dispersion. It is a measure of spread of data about the mean. SD is the square root of sum of squared deviation from the mean divided by the number of observations.
Which is used to describe the amount of spread dispersion?The variance and the standard deviation are measures of the spread of the data around the mean. They summarise how close each observed data value is to the mean value.
How do you describe the spread or dispersion in a probability distribution?In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range.
What is the variability of the items in a distribution?Variability is most commonly measured with the following descriptive statistics: Range: the difference between the highest and lowest values. Interquartile range: the range of the middle half of a distribution. Standard deviation: average distance from the mean.
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