Measures of Dispersion

Measuresof Dispersion

Whereasmean, mode, and median are measures of central tendency, there arealso measures of dispersion or spread in statistics, referred to asvariability of scatter. Measures of dispersion include standarddeviation, variance, interquartile range, and range. They measure thedegree to which a statistical data is either squeezed together orscattered. The most commonly used are range, interquartile range,variance, and standard deviation.

Rangeshows the difference between the highest and the lowest figure orentry. The lowest in this case is $32 while the highest is $2409.Therefore, the range is $2377.

Standarddeviation is calculated by first calculating the variance, which isobtained by

Where,X is the mean, M is the data, while n is the population

Populationmean equals total divide by the population size, which comes to: $(89992/60) = $1499.86

ThusApproximately $1500

Scomes to $ 592

Coefficientof skewness is obtained by,

WhereMd is median and S is standard deviation

=-0.52956

Thefirst quartile shows the 25^thpercent value while the third quartile shows the 75^thpercent value.

1srquartile=$1120

3^rdquartile=$1913

Interpretationsand Conclusion

Thestandard deviation of $ 592 in the bank balances here shows that thevalues are values in the population are $592 close or far from thepopulation mean. In this case, they are not so concentrated aroundthe mean or average. The big margin in the standard deviation of bankbalances could be informed by outlies, i.e. figures that are tooextreme like $32 and $2409

Thedistribution is negatively skewed or skewed to the left. Thus thedistribution is in such a way that those balances that fall below themean are more than those that fall above the mean