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Are any of the measures of dispersion among the range the variance and the standard deviation resistant explain choose the correct answer below?
Question: Are any of the measures of dispersion among the range, the variance, and the standard deviation, resistant? … Yes, the variance is resistant because it has squared units, so is always positive. OB. No, all of these measures of dispersion are affected by extreme values.
Dispersion: Variance, Standard Deviation A variance measures the degree of spread (dispersion) in a variable’s values.
Range, interquartile range, and standard deviation are the three commonly used measures of dispersion.
Absolute measures include Range, quartile deviation, mean deviation, and standard deviation. Relative measures include coefficients of range, quartile deviation, variation, and mean deviation. Hence, Quartile is not the measure of dispersion.
The interquartile range is a resistant measure of dispersion. The upper and lower fences can be used to identify potential outliers.
T/F: The standard deviation is a resistant measure of spread. False. Since extreme values will increase the standard deviation greatly, the standard deviation cannot be a resistant measure of spread. … This makes intuitive sense because the standard deviation measures the spread of the data from the mean.
- Standard deviation looks at how spread out a group of numbers is from the mean, by looking at the square root of the variance.
- The variance measures the average degree to which each point differs from the mean—the average of all data points.
What is the relationship between the standard deviation and the variance? The variance is equal to the standard deviation, squared.
Standard deviation is statistics that measure the dispersion of a dataset relative to it is mean and its calculated as the square root of variance.it is calculated as the square root of variance by determining the variation between each data point relative to the mean.
The RANGE is a bad measure of dispersion because it is affected by outliers.It only uses the two extreme values in a dataset. By using the two extreme values in a dataset, it is quite wasteful of resources because all the values in between the maximum and minimu are neglected.
- Measure # 1. Range:
- Measure # 2. Quartile Deviation:
- Measure # 3. Average Deviation (A.D.) or Mean Deviation (M.D.):
- Measure # 4. Standard Deviation or S.D. and Variance:
The standard deviation and variance are the most commonly used measures of dispersion in the social sciences because: Both take into account the precise difference between each score and the mean.
Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out. A standard deviation close to zero indicates that data points are close to the mean, whereas a high or low standard deviation indicates data points are respectively above or below the mean.
Variance is a numerical value that describes the variability of observations from its arithmetic mean. Standard deviation is a measure of the dispersion of observations within a data set relative to their mean. Variance is nothing but an average of squared deviations.
The range, interquartile range and standard deviation are three of the measures of variation. So, we’re left with the mode, which is actually a measure of central tendency, not a measure of variation. Thus, option C is correct.