Measures of Dispersion
| 1. | What is Measure of Dispersion? |
| 2. | Types of Measures of Dispersion |
| 3. | Absolute Measures of Dispersion |
| 4. | Relative Measures of Dispersion |
| 5. | Measures of Dispersion Formula |
Why do we use relative measures of dispersion?
Since relative measures of dispersion are free from the units in which the values have been expressed, they can be compared even across different groups having different units of measurement. Let us also talk about the method of drawing an inference.
What is an absolute measure of dispersion?
An absolute measure of dispersion contains the same unit as the original data set. Absolute dispersion method expresses the variations in terms of the average of deviations of observations like standard or means deviations. It includes range, standard deviation, quartile deviation, etc. The types of absolute measures of dispersion are:
What is dispersion in statistics?
What is Dispersion in Statistics? Dispersion is the state of getting dispersed or spread. Statistical dispersion means the extent to which a numerical data is likely to vary about an average value. In other words, dispersion helps to understand the distribution of the data.
How do you find the coefficient of relative dispersion?
The coefficient of standard deviation, the analogous measure of relative dispersion, is just the standard deviation divided by the arithmetic mean. To give it as a percentage rather than a ratio, multiply by 100%. Click to see full answer. Considering this, what is relative dispersion?
What is a relative measure of dispersion?
The coefficient of variation is a relative measure of dispersion.
What is relative measure of dispersion Class 11?
Relative Measure of Dispersion The relative measures of dispersion are used to compare the distribution of two or more data sets. This measure compares values without units. Common relative dispersion methods include: Co-efficient of Range.
What do you mean by absolute and relative measure of dispersion?
Absolute measure of Dispersion has unit of measure like kg., cm, Rs., etc. Whereas Relative Measure is a ratio ; it is a pure number without uniit of measure.Absolute measure will tell you about individual groups; on the other hand Relative Measure will hepl to compare between two or more groups or sets of data.
What do you mean by relative measures?
Relative measurement is a method for deriving ratio scales from paired comparisons represented by absolute numbers.
What is the relative measure of dispersion Mcq?
Solution: The relative measures of dispersion are expressed in percentage. These are used to compare two or more series which are expressed in different units. standard deviation.
Which is not relative measure of dispersion?
Relative measures include coefficients of range, quartile deviation, variation, and mean deviation. Hence, Quartile is not the measure of dispersion.
What is meant by absolute measures of dispersion?
Absolute Measure of Dispersion. An absolute measure of dispersion contains the same unit as the original data set. Absolute dispersion method expresses the variations in terms of the average of deviations of observations like standard or means deviations. It includes range, standard deviation, quartile deviation, etc.
What is meant by absolute and relative measures?
Absolute measures includes range, quartile deviation, mean deviation and standard deviation. Relative measures includes coefficient of range, coefficient of quartile deviation, coefficient of mean deviation and coefficient of standard deviation.
Why Is Dispersion Important in Statistics?
The measures of dispersion are important as it helps in understanding how much data is spread (i.e. its variation) around a central value.
How To Calculate Dispersion?
Dispersion can be calculated using various measures like mean, standard deviation, variance, etc.
What is the Variance of the values 3, 8, 6, 10, 12, 9, 11, 10, 12, 7?
The variance of the following numbers will be 7.36.
What are the examples of dispersion measures?
Standard deviation, Range, Mean absolute difference, Median absolute deviation, Interquartile change, and Average deviation are examples of measure...
What is the purpose of dispersion in statistics?
In statistics, the measures of dispersion help to interpret the variability of data i. e. to know how much homogenous or heterogeneous the data is. In simple terms, it shows how squeezed or scattered the variable is.
What is absolute dispersion?
An absolute measure of dispersion contains the same unit as the original data set. Absolute dispersion method expresses the variations in terms of the average of deviations of observations like standard or means deviations. It includes range, standard deviation, quartile deviation, etc.
What is the state of getting dispersed?
Dispersion is the state of getting dispersed or spread. Statistical dispersion means the extent to which a numerical data is likely to vary about an average value. In other words, dispersion helps to understand the distribution of the data.
When are coefficients of dispersion calculated?
The coefficients of dispersion are calculated (along with the measure of dispersion) when two series are compared, that differ widely in their averages. The dispersion coefficient is also used when two series with different measurement units are compared. It is denoted as C.D.
What is mean deviation?
Mean and Mean Deviation: The average of numbers is known as the mean and the arithmetic mean of the absolute deviations of the observations from a measure of central tendency is known as the mean deviation (also called mean absolute deviation).
What are absolute measures of dispersion?
The absolute measures of dispersion accurately display the dispersion of data in a given series. However, a drawback to them is that we cannot use them to compare dispersion for series that are in different units. The concept of relative measures of dispersion overcomes this limitation.
What is a Lorenz curve?
Lorenz curve is a type of absolute measure of dispersion. Unlike others, it is a graphical measure of dispersion. Lorenz curve graphically represents the actual curve and a line of equal distribution and exhibits the deviation between these two.
Relative Measures of Dispersion
A given series of data is accurately exhibited by the absolute measures of dispersion. But one of the major demerits of this is that if there is a need to compare dispersion for a series of different units then it cannot be used. The above-mentioned comparison can be done with relative dispersion.
Coefficient of Quartile Deviation
First and third quartile for individual series is calculated by the formula:
Coefficient of Mean Deviation
Coefficient of Mean Deviation About Mean: (mean deviation about mean)/arithmetic mean.
Lorenz Curve
The absolute measure of dispersion is measured graphically by the Lorenz curve. The actual curve and a line of equal distribution are represented graphically through the Lorenz curve. It displays the deviation between these two.
Did You Know?
In the frequency distribution series, Q2 or the second quartile is also known as the median.
Definition of Measures of Dispersion
Dispersion in simple words means “scattered” or “spread”. In statistical data, dispersion refers to the extent to which the data is distributed. It can either be tightly clustered or widely scattered.
Sample questions
Question. Following table shows the result values for companies A and B.
Coefficient of Dispersion
Based on several metrics of dispersion, the coefficients of dispersion (C.D.) are calculated. 1. C.D. based on Range = Xmax – X min X max + X min 2. C.D. based on Quartile deviation = Q3 – Q1 Q3 + Q1 3. C.D. based on Mean deviation = MeanDeviation A 4. C.D. based on Standard deviation = S. D. Mean 5. Coefficient of Variation = S. D. Mean × 100
Summary
In this article, we have learnt about the measures of dispersion. Dispersion refers to how many values in a distribution deviate from the average. It tells us how different individual items are from one another and from the centre value.
FAQs
Q.1. What are the 4 measures of dispersion? Ans: Dispersion measures describe how widely the data is spread out. Range, quartile deviation, Mean deviation, and standard deviation are the 4 measures of dispersion.