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Measures of Dispersion quiz questions and answers, measures of dispersion trivia questions PDF to practice business statistics test 9 for online certification. Learn average deviation measures MCQs , "Measures of Dispersion" quiz questions and answers for admission and merit scholarships test. Learn average deviation measures, measuring dispersion, relationship: measures of deviation, interquartile range of deviation, variance and standard deviation career test for online business administration degree classes.
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Quantitative Methods 1 Reading 7. Statistical Concepts and Market Returns Subject 6. Measures of Dispersion. Why should I choose AnalystNotes? AnalystNotes specializes in helping candidates pass. Find out more. Subject 6. A central tendency is a measure of the reward of an investment and dispersion is a measure of investment risk.
There are two types of dispersions: Absolute dispersion is the amount of variability without comparison to any benchmark. Measures of absolute dispersion include range, mean absolute deviation, variance, and standard deviation. Relative dispersion is the amount of variability in comparison to a benchmark. Measures of relative dispersion include the coefficient of variance.
The range is the simplest measure of spread or dispersion. It is equal to the difference between the largest and the smallest values. The range can be a useful measure of spread because it is so easily understood. However, it is very sensitive to extreme scores because it is based on only two values. It also cannot reveal the shape of the distribution. The range should almost never be used as the only measure of spread, but it can be informative if used as a supplement to other measures of spread, such as the standard deviation or semi-interquartile range.
The mean absolute deviation MAD is the arithmetic average of the absolute deviations around the mean. In calculating the MAD, we ignore the signs of deviations around the mean. Remember that the sum of all the deviations from the mean is equal to zero. To get around this zeroing-out problem, the mean deviation uses the absolute values of each deviation. MAD is superior to the range as a measure of dispersion because it uses all the observations in the sample. However, the absolute value is difficult to work with mathematically.
The variance is a measure of how spread out a distribution is. It is computed as the average squared deviation of each number from its mean. Since samples are usually used to estimate parameters, s 2 is the most commonly used measure of variance. The formula for the sample variance is nearly the same as that for the population variance except for the use of the sample mean, X, and the denominator. In the case of the population variance, we divide by the size of the population, N.
For the sample variance, however, we divide by the sample size minus 1, or N - 1. In the math of statistics, using only N in the denominator when using a sample to represent its population will result in underestimating the population variance, especially for small sample sizes. This systematic understatement causes the sample variance to be a biased estimator of the population variance.
By using N - 1 instead of N in the denominator, we compensate for this underestimation. The major problem with using the variance is the difficulty interpreting it. The variance, unlike the mean, is in terms of units squared.
How does one interpret squared percentages or squared dollars? The solution to this problem is to use the standard deviation. The formula for the standard deviation is very simple: it is the square root of the variance. This is the most commonly used measure of spread. The variance indicates the adequacy of the mean as representative of the population by measuring the deviation from expectation.
Basically, the variance and the standard deviation are measures of the average deviation from the mean. An important attribute of the standard deviation as a measure of spread is that if the mean and standard deviation of a normal distribution are known, it is possible to compute the percentile rank associated with any given score.
The standard deviation has proven to be an extremely useful measure of spread in part because it is mathematically tractable. Many formulas in inferential statistics use the standard deviation.
A direct comparison of two or more measures of dispersion may be difficult. For example, the difference between the dispersion for monthly returns on T-bills and the dispersion for a portfolio of small stocks is not meaningful because the means of the distributions are far apart.
In order to make a meaningful comparison, we need a relative measure, to standardize the measures of absolute dispersion. It is often useful to compare the relative variation in data sets that have different means and standard deviations, or that are measured in different units. Relative dispersion is the amount of variability present in comparison to a reference point or benchmark. The coefficient of variation CV is used to standardize the measure of absolute dispersion.
It is defined as: It gives a measure of risk per unit of return, and an idea of the magnitude of variation in percentage terms. It allows us direct comparison of dispersion across data sets. The lower the CV, the better; investments with low CV numbers offer less risk per unit of return. This measurement is also called relative standard deviation RSD. Note that because s and X-bar have the same units associated with them, the units effectively cancel each other out, leaving a unitless measure which allows for direct comparison of dispersions, regardless of the means of the data sets.
The CV is not an ideal measure of dispersion. What if the expected return is zero!? Generally, the standard deviation is the measure of choice for overall risk and beta for individual assets. Example The mean monthly return on T-bills is 0. LOS Quiz. Subject marked as complete. Subject marked as incomplete. Subject bookmarked for review later on your dashboard. Bookmark removed from your dashboard. Download study notes in a PDF file immediately.
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My Flashcard:. Gooner7 What does variance even tell you? The levered beta i. You have a wonderful website and definitely should take some credit for your members' outstanding grades. Colin Sampaleanu. My Own Flashcard No flashcard found. Add a private flashcard for the subject. Beta - essentially, measures the sensitivity of the stock's returns to that of the market portfolio i.
Quantitative Methods 1 Reading 7. Statistical Concepts and Market Returns Subject 6. Measures of Dispersion. Why should I choose AnalystNotes? AnalystNotes specializes in helping candidates pass. Find out more. Subject 6.
These solutions for Measures Of Dispersion are extremely popular among Class 11 Commerce students for Economics Measures Of Dispersion Solutions come handy for quickly completing your homework and preparing for exams. Find the range and coefficient of range of the following: Size of shoes 6 7 8 9 10 11 12 13 No. Size of Shoes No.
Learn frequency distribution, measures of central tendency, measures of dispersion test prep for online study. Free math student portal for online learning basic statistics quiz questions for high school graduation certificate. MCQ : Statistically, the spread or scatterness of observations in a data is called.
In this case, all three measures are useful. We would understand that means. Find the mean of the following set of numbers: i 6, 9, 11, 12 and 7 ii 11, 14, 23, 26, 10, 12, 18 and 6 Solution: Question 2. Question 1.
These solutions for Measures Of Dispersion are extremely popular among Class 11 Commerce students for Economics Measures Of Dispersion Solutions come handy for quickly completing your homework and preparing for exams. A measure of dispersion is a good supplement to the central value in understanding a frequency distribution. The study of the averages is only one sided distribution story. In order to understand the frequency distribution fully, it is essential to study the variability of the observations. The average measures center of the data whereas the quantum of the variation is measured by the measures of dispersion like range, quartile deviation, mean deviation and Standard Deviation. For example, if a country has very high income group people and very low income group people, then we can say that the country has large income disparity. Standard Deviation is the best measure of dispersion as it satisfies the most essentials of the good measure of dispersion.
Section Measures of Dispersion. The measures of central tendency we studied in the last section (mean, Answer: Standard deviation = hours.
Exercise 8. Find the range and coefficient of range of the following data. If the range and the smallest value of a set of data are Calculate the range of the following data. A teacher asked the students to complete 60 pages of a record note book.
Learn interquartile range of deviation MCQs , "Measures of Dispersion" quiz questions and answers for admission and merit scholarships test. Learn interquartile range of deviation, mean absolute deviation, squared deviation, classification: measures of dispersion, relationship: measures of deviation career test for BA in business administration. Practice jobs' assessment test, online learning interquartile range of deviation quiz questions for online business management degree programs. MCQ : If mean absolute deviation of set of observations is 8. MCQ : The sum of all the squared deviations is divided by the total number of observations to calculate.
Quantitative Methods 1 Reading 7. Statistical Concepts and Market Returns Subject 6. Measures of Dispersion. Why should I choose AnalystNotes? AnalystNotes specializes in helping candidates pass.
Define dispersion. Dispersion is the extent to which values in a distribution vary from the average of the distribution. Name the two types of measures.
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