Measures of Dispersion: Definition, Types & Key Questions
Measures of dispersion are essential in statistics and economics for understanding how much individual data values differ from their average. This concept is important for school and competitive exams, as well as for analyzing data in business decisions and daily life. At Vedantu, we simplify measures of dispersion to help students master exam questions and apply concepts in real scenarios.
| Measure of Dispersion | What It Shows | Calculation | Applies To |
|---|---|---|---|
| Range | Difference between highest and lowest value | Highest value - Lowest value | Simple data sets |
| Mean Deviation | Average deviation from mean or median | Sum of absolute deviations / Number of values | Individual, discrete, and continuous series |
| Standard Deviation | Average squared deviation from mean | Square root of variance | All types of numerical data |
| Quartile Deviation | Spread of middle 50% of data | (Q3 - Q1) / 2 | Grouped and ungrouped data |
Measures of Dispersion: Concepts and Importance
Measures of dispersion give insight into the variability or spread of data values in a series. These tools help compare consistency or risk between different data sets, such as wages, prices, or test scores, making them vital for effective analysis in commerce and economics.
Types of Measures of Dispersion
There are two main types of measures of dispersion: absolute and relative. Absolute measures (like standard deviation, mean deviation, and range) use the original units of data, while relative measures (like coefficient of variation) provide comparisons as ratios or percentages, even if data have different units or scales.
- Range
- Mean Deviation
- Standard Deviation
- Quartile Deviation
- Coefficient of Variation (relative measure)
MCQs on Measures of Dispersion (With Answers)
| Question | Options | Answer |
|---|---|---|
| Which of the following are methods under measures of dispersion? | a) Standard deviation b) Mean deviation c) Range d) All of the above |
d |
| Which is a characteristic of a good measure of dispersion? | a) Easy to calculate b) Based on all observations c) Not affected by sampling fluctuations d) All of the above |
d |
| If all observations in a data set are multiplied by five, the standard deviation will: | a) Decrease by five b) Increase by five c) Become half d) Be multiplied by five |
d |
| The coefficient of variation is used to express: | a) Standard deviation b) Quartile deviation c) Mean deviation d) None of the above |
a |
| Standard deviation deviations are calculated from: | a) Mode b) Median c) Quartile d) Mean |
d |
| Which are types of measures of dispersion? | a) Nominal, Real b) Nominal, Relative c) Real, Relative d) Absolute, Relative |
d |
| The value of standard deviation can never be: | a) Negative b) Zero c) Larger than variance d) None of the above |
a |
| The average of squared deviations from the mean is called: | a) Quartile deviation b) Standard deviation c) Variance d) None of the above |
c |
| Which is not a characteristic of a good measure of dispersion? | a) Rigidly defined b) Based on extreme values c) Capable of mathematical treatment d) None of the above |
d |
| What cannot be calculated for open-ended distributions? | a) Standard deviation b) Mean deviation c) Range d) None of the above |
b |
| The Lorenz Curve is a technique used to show: | a) Inequality of wealth b) Unemployment c) Equality of wealth d) None of the above |
a |
| The Lorenz curve was developed in 1905 by: | a) Dr. Max O. Lorenz b) Dr. Max C. Lorenz c) Dr. Max M. Lorenz d) Dr. Max S. Lorenz |
a |
| The standard deviation of 90 observations is 105. If all values decrease by 9, the new standard deviation is: | a) 96 b) 100 c) 105 d) None of the above |
c |
| If average wage is Rs. 200 (SD 40), and wages increase by 20%, what is the new mean wage? | a) Unchanged b) Increased by 20% c) Rs. 240 d) Both b and c |
d |
| Securing 97 percentile in an exam means your position is below: | a) 97 percent b) 3 percent c) 90 percent d) None of the above |
b |
| Which measure of dispersion may be negative? | a) Mean deviation b) Range c) Standard deviation d) None of the above |
b |
| The range represents: | a) The lowest number b) The highest number c) The middle number d) Difference between the lowest and highest number |
a |
| The square of standard deviation is: | a) Square deviation b) Mean square deviation c) Variance d) None of the above |
c |
| Example of real-world use of range: | a) Stock price fluctuation b) Weather forecast c) Quality control d) All of the above |
d |
| High scatter in a distribution indicates: | a) High uniformity b) Outliers c) Low uniformity d) None of the above |
b |
Real-Life Application of Measures of Dispersion
In daily business, measures of dispersion are used to check consistency in employee salaries, monitor fluctuations in product quality, and analyze risk in share prices. For example, quality control in factories relies on standard deviation, while stock market analysis often uses range to show price fluctuations.
Comparison Table: Absolute and Relative Measures of Dispersion
| Type | Examples | When to Use | Formula Basis |
|---|---|---|---|
| Absolute | Range, Mean deviation, Standard deviation, Quartile deviation | Comparing data with same units | Original units of data |
| Relative | Coefficient of variation, Coefficient of range | Comparing data with different units/scales | Proportion or percentage |
Downloads and Resources for Exam Practice
- Free MCQs PDF: Download a worksheet of Measures of Dispersion MCQs with Answer Key for your exam revision.
- Conceptual notes: Review related topics like Relative Measures of Dispersion and Lorenz Curve.
Key Internal Commerce Links
- Tabular Presentation of Data
- Use of Statistical Tools
- Measures of Central Tendency (Median)
- Difference Between Random Sampling and Non-Random Sampling
- Index Numbers
To sum up, measures of dispersion help compare, analyze, and interpret data sets by showing how values spread around the average. Knowing the types, formulas, and applications is essential for exams, business analytics, and everyday understanding of statistics in commerce. Use Vedantu's resources to deepen your understanding and score better in tests.
FAQs on MCQs On Measures Of Dispersion: Practice With Answer Keys
1. What are the main measures of dispersion?
Measures of dispersion describe the spread or variability within a dataset. The four main measures are range, mean deviation, standard deviation, and quartile deviation. These help analyze data spread and are crucial in statistics and economics.
2. Is mode a measure of dispersion?
No, mode is a measure of central tendency, not dispersion. It identifies the most frequent value but doesn't reflect the data's spread or variability, unlike standard deviation or range which are measures of dispersion. Understanding this distinction is key for commerce exams.
3. What are the four main measures of dispersion?
The four main measures of dispersion are the range, mean deviation, standard deviation, and quartile deviation. Each method offers a different perspective on how data points are scattered around the average (measures of central tendency), useful for various applications in economics and statistics.
4. Why are measures of dispersion important?
Measures of dispersion are vital because they show data variability. Understanding the spread helps in:
- Risk assessment in finance (e.g., stock market volatility).
- Quality control in manufacturing (e.g., consistency of product dimensions).
- Data analysis for informed decision-making in various fields.
They complement measures of central tendency (mean, median, mode) providing a complete picture of the data.
5. What is not a measure of dispersion?
Measures of central tendency, such as the mean, median, and mode, are not measures of dispersion. They describe the central location of data, not its spread or variability. In contrast, range, standard deviation, and quartile deviation are key measures of dispersion.
6. What is a measure of dispersion?
A measure of dispersion in statistics quantifies the spread or variability of a dataset. It shows how much the data points are scattered around a central value (like the mean or median). Common measures include range, variance, standard deviation, and quartile deviation. Understanding dispersion is crucial for interpreting data effectively.
7. How do you solve MCQ on dispersion?
Solving MCQs on dispersion requires understanding the different measures (range, mean deviation, standard deviation, quartile deviation) and their calculations. Practice applying these measures to different datasets, focusing on identifying the spread and variability within the data. Review formulas and examples before the exam.
8. Where can I download MCQ on measures of dispersion with answers?
Downloadable resources with MCQs on measures of dispersion and answers are available online from educational websites. These often include practice worksheets and PDFs to aid self-study and exam preparation. Look for reputable sources aligned with your syllabus.
9. Measures of dispersion include the following with the exception of?
The options given will likely include measures of dispersion like range, standard deviation, mean deviation etc. The exception would be a measure of central tendency such as mean, median or mode, which describe the center of the data, not its spread.
10. Can standard deviation be negative?
No, standard deviation cannot be negative. It's always either zero (when all data points are identical) or a positive value, representing the amount of data spread around the mean. A higher standard deviation indicates greater variability.
