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Which one of the following statements is NOT true?
- a)The measure of skewness is dependent upon the amount of dispersion
- b)In a symmetric distribution, the values of mean, mode and median are the same
- c)In a positively skewed distribution; mean > median > mode
- d)In a negatively skewed distribution; mode > mean > median
Correct answer is option 'D'. Can you explain this answer?
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Which one of the following statements is NOT true?a)The measure of ske...
Explanation:
Skewness is a measure of the asymmetry of a probability distribution. It is used to determine the direction and degree of deviation from normal distribution. A distribution can be positively skewed, negatively skewed, or symmetric. The following statements explain the true statement and the false statement.
a) The measure of skewness is dependent upon the amount of dispersion
The measure of skewness is dependent upon the amount of dispersion. It indicates the degree to which a distribution is not symmetrical. Skewness is calculated as the third standardized moment, where the values are normalized by the standard deviation. The formula for skewness is:
Skewness = 3 * (Mean - Median) / Standard Deviation
The measure of skewness is influenced by the amount of dispersion in the data. A distribution with more dispersion will have a greater degree of skewness.
b) In a symmetric distribution, the values of mean, mode and median are the same
In a symmetric distribution, the values of mean, mode, and median are the same. A symmetric distribution is a distribution in which the mean, median, and mode are equal. In other words, the distribution is evenly distributed around the central value. The most common example of a symmetric distribution is the normal distribution.
c) In a positively skewed distribution; mean < median="" />< />
In a positively skewed distribution, the mean is less than the median, which is less than the mode. The tail of the distribution is longer on the right-hand side, and the distribution is pulled towards the right. This is because there are more small values on the left-hand side of the distribution.
d) In a negatively skewed distribution; mode > median > mean
The false statement is that in a negatively skewed distribution, the mode is greater than the mean, which is greater than the median. The correct statement is that in a negatively skewed distribution, the mode is less than the median, which is less than the mean. The tail of the distribution is longer on the left-hand side, and the distribution is pulled towards the left. This is because there are more large values on the left-hand side of the distribution.
Skewness is a measure of the asymmetry of a probability distribution. It is used to determine the direction and degree of deviation from normal distribution. A distribution can be positively skewed, negatively skewed, or symmetric. The following statements explain the true statement and the false statement.
a) The measure of skewness is dependent upon the amount of dispersion
The measure of skewness is dependent upon the amount of dispersion. It indicates the degree to which a distribution is not symmetrical. Skewness is calculated as the third standardized moment, where the values are normalized by the standard deviation. The formula for skewness is:
Skewness = 3 * (Mean - Median) / Standard Deviation
The measure of skewness is influenced by the amount of dispersion in the data. A distribution with more dispersion will have a greater degree of skewness.
b) In a symmetric distribution, the values of mean, mode and median are the same
In a symmetric distribution, the values of mean, mode, and median are the same. A symmetric distribution is a distribution in which the mean, median, and mode are equal. In other words, the distribution is evenly distributed around the central value. The most common example of a symmetric distribution is the normal distribution.
c) In a positively skewed distribution; mean < median="" />< />
In a positively skewed distribution, the mean is less than the median, which is less than the mode. The tail of the distribution is longer on the right-hand side, and the distribution is pulled towards the right. This is because there are more small values on the left-hand side of the distribution.
d) In a negatively skewed distribution; mode > median > mean
The false statement is that in a negatively skewed distribution, the mode is greater than the mean, which is greater than the median. The correct statement is that in a negatively skewed distribution, the mode is less than the median, which is less than the mean. The tail of the distribution is longer on the left-hand side, and the distribution is pulled towards the left. This is because there are more large values on the left-hand side of the distribution.
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Which one of the following statements is NOT true?a)The measure of skewness is dependent upon the amount of dispersion b)In a symmetric distribution, the values of mean, mode and median are the same c)In a positively skewed distribution; mean median mode d)In a negatively skewed distribution; mode mean median Correct answer is option 'D'. Can you explain this answer?
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