Central tendency and variability

Central tendency is the measure of the probability of numbers and distribution to the given location while variability is the distribution of statistical data from the extent of average points to the extent of diverging points in addition to the extent from each other points of data. Central tendency is measured with three indexes which are the mean, the mode, and the median while variability is measured by the range, the variance, the inter-quartile range and standard deviation.

The mean is also known as average and it is the measure of central tendency. The mean is calculated as a sum of all values in an extent of data points set dividing it with the extent of points given. The mean of data located is essentially a model which has the common values. Actual values are not given by the mean as it is observed in the data set but it is very important because it minimizes errors of the data set values which are predicted. The mean has advantage and disadvantage in it because as on advantage it produces the lower amount of error to the value predicted. The mean disadvantage is that it produce unusual values that are mainly susceptible as it is compared to the values of values of the data set which might be small or large value hence influencing the outliers. Mean is appropriate in central tendency to measure ratio or interval that is not tilted (Weisberg, 1992).

Weisberg (1992) stated that mode is the highest percentage of a value of data set. The mode is the best when it comes to the comparison of values given and find only one value is greatest. But it is a big problem when the mode is used to measure central tendency it occurs in two values that are greatest but with the same arithmetic number. At this point of two greatest numbers, mode can fail to give the appropriate measure of central tendency. It is more suitable to use mode in nominal because it will give out an appropriate measure to the central tendency.

The median is given by the middle score when values set arranged from the smallest to the largest. The median is not much affected by tilted and outliers because the values are arranged from the lowest to the largest creating susceptible values when they are compared. Median is more appropriate in measuring central tendency when it comes to ordinal and ratio or interval that is tilted (Weisberg, 1992).

In the measure of variability, rage is the appropriate measure when it comes to dispersion and the difference of values between the smallest and the largest values in a data set. The range is calculated by finding a difference of smallest values  from the largest value as it is in order magnitude. The range is the simplest and useful measure of variability when a whole data set was given is evaluated. The range is not only useful in evaluating but also useful in comparing the dataset spread (Weisberg, 1992).

Variance is the difference of score from the mean computed giving out the square root. Variance measures the middle of the distribution in the given values of a dataset. Variance is calculated with the right formula and placed in the right field given that value in the dataset is at the bottom of the field. Variance is useful in measuring variability since it balances the distribution of given values in a dataset (Weisberg, 1992).

According to Weisberg (1992) inter-quartile consists of two quartiles which are upper quartile and lower quartile. The inter-quartile is divided into two half ending up with upper and lower quartiles. These two quartiles are indicated when the values arranged into order magnitude. The upper lower quartile lies between the middle and the upper quartile while upper quartile lies between the middle and the lower quartile. Quartile measures variability by indicating the middle of percentage in the extent values given in the dataset which also is related to the median. The inter-quartile is found when the lower quartile is subtracted from upper quartile. Inter-quartile is appropriate in measuring variability because it considers variable of a datasheet.

Standard deviation is found by finding the square root of the variance. Standard deviation requires more computation because means and variance must be computed before finding the root. The standard deviation is the most appropriate measure of variability because it computes all measure and takes all value of dataset varies from the mean. Standard deviation has to be sure since it takes into account and has to be considered in the entire population given appropriate formula on it (Weisberg, 1992).

In the mean, the mode and the median measures of central tendency, mean is advisable to be used in the case of ratio and interval which is not tilted. Whereas mode is the most appropriate in calculating the nominal in central tendency. And the median is used in computing ratio or interval that are tilted and ordinal. In the variability, we have to see the range is appropriate to be used in the case of dispersion. Variance is appropriate in computing distribution of values in a dataset. Inter-quartile is the best in measuring variability while considering the comparison of the spreadsheet. The last measure of variability is standard deviation is appropriate in measuring the entire dataset spreadsheet using appropriate formula to compute it.

 

 

 

 

Reference

Weisberg, H. F. (1992). Central Tendency and Variability, Sage University Paper Series on         Quantitative Applications in the Social Sciences.