The relative measures of dispersion are expressed ina)numbers.b)same units.c)percentage.d)quartiles.Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Relative measures of dispersion are calculated as ratios or percentages; for example, one relative measure of dispersion is the ratio of the standard deviation to the mean. Relative measures of dispersion are always dimensionless, and they are particularly useful for making comparisons between separate data sets or different experiments that might use different units. They are sometimes called coefficients of dispersion.

Answer

The relative measures of dispersion are expressed in percentage. These are used to compare two or more series which are expressed in different units.

Answer

Explanation:

The relative measures of dispersion are used to determine the spread or variability of a dataset. They provide information about how the data points are distributed around the central tendency measures such as mean, median, or mode. These measures are expressed in percentage (%).

Relative Measures of Dispersion:

1. Coefficient of Variation (CV): The coefficient of variation is a relative measure of dispersion that is used to compare the variability of different datasets, especially when they have different units or scales of measurement. It is expressed as a percentage (%). The formula for calculating the coefficient of variation is:

CV = (Standard Deviation / Mean) * 100

The coefficient of variation allows for the comparison of the relative variability of datasets with different means.

2. Relative Standard Deviation (RSD): The relative standard deviation is another relative measure of dispersion that is used to compare the variability of datasets. It is expressed as a percentage (%). The formula for calculating the relative standard deviation is:

RSD = (Standard Deviation / Mean) * 100

The relative standard deviation provides information about the relative spread of the data points around the mean.

3. Percentiles: Percentiles are a type of relative measure of dispersion that divide a dataset into equal parts. For example, the quartiles divide a dataset into four equal parts, with each quartile representing 25% of the data. Percentiles provide information about the relative position of a data point within a dataset.

- First Quartile (Q1): It represents the 25th percentile, dividing the dataset into the lower 25% and upper 75%.
- Second Quartile (Q2): It represents the 50th percentile, which is equal to the median. It divides the dataset into the lower 50% and upper 50%.
- Third Quartile (Q3): It represents the 75th percentile, dividing the dataset into the lower 75% and upper 25%.

Conclusion:

The relative measures of dispersion, such as the coefficient of variation, relative standard deviation, and percentiles (e.g., quartiles), are expressed in percentage (%). These measures allow for the comparison of the spread or variability of datasets, regardless of their units or scales of measurement.

Similar Commerce Doubts

What does a measure of dispersion reveal about data?

Which of the following is NOT a relative measure of dispersion?

Which statistical measure is used to describe the variability or spread of data points?

Which statistical measure helps in understanding the typical or central value of a dataset?

Measure of dispersion considering only extreme values is called

Top Courses for CommerceView all

Chapter Notes for Commerce

Economics Class 12

Economics Class 11

NCERT Books & Solutions for Commerce

Economics for CBSE Class 12 Board Examinations

Top Courses for Commerce

Top Courses for Commerce

Related Content

Commerce Courses

Other Courses

How To Prepare?

Related Exams

Company