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What do you mean by measures of central tendency and dispersion?
Common measures of central tendency are the mean, median, mode. Common measures of dispersion are range, interquartile range, variance, standard deviation.
Why is standard deviation called the best of all measures of dispersion?
standard deviation is the best measure of dispersion because.. a)It measure the absolute dispersion b)It is most frequentlyused as prossesses almost all the the qualities that a good measure of variation have. c)It is beased on all observation. d)It is rigidly defined. e)It is capable of further algebraic treatment. f)It is least affected by the fluctuation of sampling.
Why standard deviation is more often used than variance?
Both variance and standard deviation are measures of dispersion or variability in a set of data. They both measure how far the observations are scattered away from the mean (or average). While computing the variance, you compute the deviation of each observation from the mean, square it and sum all of the squared deviations. This somewhat exaggerates the true picure because the numbers become large when you square them. So, we take the square root of the variance (to compensate for the excess) and this is known as the standard deviation. This is why the standard deviation is more often used than variance but the standard deviation is just the square root of the variance.
What determines the standard deviation to be high?
Standard deviation is a measure of the scatter or dispersion of the data. Two sets of data can have the same mean, but different standard deviations. The dataset with the higher standard deviation will generally have values that are more scattered. We generally look at the standard deviation in relation to the mean. If the standard deviation is much smaller than the mean, we may consider that the data has low dipersion. If the standard deviation is much higher than the mean, it may indicate the dataset has high dispersion A second cause is an outlier, a value that is very different from the data. Sometimes it is a mistake. I will give you an example. Suppose I am measuring people's height, and I record all data in meters, except on height which I record in millimeters- 1000 times higher. This may cause an erroneous mean and standard deviation to be calculated.
Annualized standard deviation?
http://www.hedgefund.net/pertraconline/statbody.cfmStandard Deviation -Standard Deviation measures the dispersal or uncertainty in a random variable (in this case, investment returns). It measures the degree of variation of returns around the mean (average) return. The higher the volatility of the investment returns, the higher the standard deviation will be. For this reason, standard deviation is often used as a measure of investment risk. Where R I = Return for period I Where M R = Mean of return set R Where N = Number of Periods N M R = ( S R I ) ¸ N I=1 N Standard Deviation = ( S ( R I - M R ) 2 ¸ (N - 1) ) ½ I = 1Annualized Standard DeviationAnnualized Standard Deviation = Monthly Standard Deviation ´ ( 12 ) ½ Annualized Standard Deviation *= Quarterly Standard Deviation ´ ( 4 ) ½ * Quarterly Data
What do you mean by measures of central tendency and dispersion?
Common measures of central tendency are the mean, median, mode. Common measures of dispersion are range, interquartile range, variance, standard deviation.
What is relative measure?
These measures are calculated for the comparison of dispersion in two or more than two sets of observations. These measures are free of the units in which the original data is measured. If the original data is in dollar or kilometers, we do not use these units with relative measure of dispersion. These measures are a sort of ratio and are called coefficients. Each absolute measure of dispersion can be converted into its relative measure. Thus the relative measures of dispersion are:Coefficient of Range or Coefficient of Dispersion.Coefficient of Quartile Deviation or Quartile Coefficient of Dispersion.Coefficient of Mean Deviation or Mean Deviation of Dispersion.Coefficient of Standard Deviation or Standard Coefficient of Dispersion.Coefficient of Variation (a special case of Standard Coefficient of Dispersion)
What are the common measures of dispersion?
Range, standard deviation, variance, root mean square, interquartile range
What is despersion?
Dispersion is an abstract quality of a sample of data. Dispersion is how far apart or scattered the data values appear to be. Common measures of dispersion are the data range and standard deviation.
What is A measure of the amount of dispersion or distance between data points is the?
A measure of the amount of dispersion or distance between data points is the standard deviation. It quantifies how much individual data points differ from the mean of the dataset. A higher standard deviation indicates greater variability, while a lower standard deviation suggests that data points are closer to the mean. Other measures of dispersion include variance and range.
A measure of the amount of dispersion or distance between data points is the?
A measure of the amount of dispersion or distance between data points is the standard deviation. It quantifies how much individual data points deviate from the mean of the dataset. A higher standard deviation indicates greater variability, while a lower standard deviation suggests that the data points are closer to the mean. Other measures of dispersion include variance and range.
What is the lowest value that standard deviation can be?
The lowest value that standard deviation can be is zero. This occurs when all the data points in a dataset are identical, meaning there is no variation among them. In such cases, the standard deviation, which measures the dispersion of data points around the mean, indicates that there is no spread.
Why standard deviation is best measure of dispersion?
standard deviation is best measure of dispersion because all the data distributions are nearer to the normal distribution.
Does the outlier affect the standard deviation?
Yes, outliers can significantly affect the standard deviation. Since standard deviation measures the dispersion of data points from the mean, the presence of an outlier can increase the overall variability, leading to a higher standard deviation. This can distort the true representation of the data's spread and may not accurately reflect the typical data points in the dataset.
Does standard deviation and mean deviation measure dispersion the same?
No. The average of the deviations, or mean deviation, will always be zero. The standard deviation is the average squared deviation which is usually non-zero.
Can you have a standard deviation of 435000?
Yes, a standard deviation of 435,000 is possible and indicates a high level of dispersion in a dataset. Standard deviation measures the amount of variation or spread in a set of values; thus, if the data points are widely spread apart from the mean, a large standard deviation can occur. This could be typical in datasets with large values, such as income or real estate prices.
How does standard deviation depend on a data?
Standard deviation measures the amount of variation or dispersion in a dataset. It quantifies how much individual data points deviate from the mean of the dataset. A larger standard deviation indicates that data points are spread out over a wider range of values, while a smaller standard deviation suggests that they are closer to the mean. Thus, the standard deviation is directly influenced by the values and distribution of the data points.
