Measures of Dispersion : - The dispersion is also known as the variability is the set of constant which would in a concise way explain variability or spread in a data. The four measures of dispersion or variability are the range, quartile deviations, average deviation and the standard deviation. The difference between two extreme observations in the given data is known as the range. It is denoted by R. In frequency distribution, R = (largest value –smallest value). It is used in statistical quality control studies rather widely. Median bisects the distribution. If we divide the distribution into four parts, we get what are called quartiles, Q(1 ),Q2 (median) and Q(3.)
The first quartile Q(1,) would have 25 % of the value below it and the rest above it; the third quartile would have 75% of values below it. Quartile deviation is defined as, Q. D. = 1/2 ( Q3-Q1). If the average is chosen a, then the average deviation about A is defined as A.D. A.D. (A) = 1/n ∑|(xi- A)| for discrete data. The Standard deviation is also called as the Root mean square deviation. The formula for the standard deviation is given as Standard deviation,σ=√(1/n ∑(xi- x ̅)^2 ) for discrete data.
The Square of the standard deviation is known as the variance. It is denoted by the square of sigma. Out of these measures, the last σ is widely used as a companion to x ̅ on who is based, when dealing with dispersion or scatter. Measure of dispersion is calculated for the data scattering. Deviation means how a value is deviated from it mean or average value. The mean of the two groups of the data may be same but their deviation may be high.
Central Tendency Measures : - The central tendency measures are also called the statistics central tendency. The clustering of data about some central value is known as the frequency distribution. The measure of central tendency is the averages or mean. The commonly used measures of central values are mean, Mode and median. The mean is the most important for it can be computed easily. The median, though more easily calculated, cannot be applied with case to theoretical analysis. Median is of advantage when there are exceptionally large and small values at the end of the distribution. The mode though easily calculated, has the least significance. It is particularly misleading in distributions which are small in numbers or highly unsymmetrical. In symmetrical distribution, the mean, median and mode coincide.
For other distributions, they are different and are known to be connected by empirical relationship. Mean – Mode = 3 (mean – median). The sum of the values of all the observations divided by the total number of observations is called the mean or average of a number of observations. The value of the middle most observations is called the median. Therefore to calculate the median of the data, it is arranged in ascending (or descending) order. The observation which is found most frequently is known as mode.
The central tendency measures and the variability or dispersion are used in the statistical analysis of the data.
The first quartile Q(1,) would have 25 % of the value below it and the rest above it; the third quartile would have 75% of values below it. Quartile deviation is defined as, Q. D. = 1/2 ( Q3-Q1). If the average is chosen a, then the average deviation about A is defined as A.D. A.D. (A) = 1/n ∑|(xi- A)| for discrete data. The Standard deviation is also called as the Root mean square deviation. The formula for the standard deviation is given as Standard deviation,σ=√(1/n ∑(xi- x ̅)^2 ) for discrete data.
The Square of the standard deviation is known as the variance. It is denoted by the square of sigma. Out of these measures, the last σ is widely used as a companion to x ̅ on who is based, when dealing with dispersion or scatter. Measure of dispersion is calculated for the data scattering. Deviation means how a value is deviated from it mean or average value. The mean of the two groups of the data may be same but their deviation may be high.
Central Tendency Measures : - The central tendency measures are also called the statistics central tendency. The clustering of data about some central value is known as the frequency distribution. The measure of central tendency is the averages or mean. The commonly used measures of central values are mean, Mode and median. The mean is the most important for it can be computed easily. The median, though more easily calculated, cannot be applied with case to theoretical analysis. Median is of advantage when there are exceptionally large and small values at the end of the distribution. The mode though easily calculated, has the least significance. It is particularly misleading in distributions which are small in numbers or highly unsymmetrical. In symmetrical distribution, the mean, median and mode coincide.
For other distributions, they are different and are known to be connected by empirical relationship. Mean – Mode = 3 (mean – median). The sum of the values of all the observations divided by the total number of observations is called the mean or average of a number of observations. The value of the middle most observations is called the median. Therefore to calculate the median of the data, it is arranged in ascending (or descending) order. The observation which is found most frequently is known as mode.
The central tendency measures and the variability or dispersion are used in the statistical analysis of the data.
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