Measuresof the Center
Measuresof the center
Onething many people pay their attention to is their paycheck.Histograms showing American weekly wages of the different gendersdepict a skew to the right as wages increase, and with most peopleearning moderate salaries. These representations provide usefulmethods of comparing the salaries of men and women. Adding morefigures could clarify the situation even more. For comparison, wewill use the median which splits the distribution by half.
Themedian salary for men was 865 dollars while that of the women was 692dollars a week about 80% of what men earned which shows the disparityin wages. Some possible causes of this variation are differences ineducation, age, and work experience. Another probable reason for thisgap is that women are concentrated in lower paying jobs. A questionarises whether these jobs are worth less income or if they pay lessbecause women primarily occupy them. This issue brought about thedebate that men and women should be paid equally for different jobsof equal worth.
Inthe year 1988, the city of Colorado Springs was at the forefront ofthis debate. The city governance evaluated all municipal jobs usingsuch criteria as working conditions, skills, and the requiredaccountability. When the jobs were numerically ranked, the cityrealized that women occupied many clerical jobs. These occupationsscored the same number of points as operations, and maintenance jobswhich were male dominated. The median wage of the men was higher thanthat of the women despite the definite similarities of these jobs. Asection of city clerical workers used this evidence to pressurize theadministration for an equitable pay structure. The numbers were hardto argue with, but the clerical workers won, and the city consentedto their demands. These changes brought about some benefits such asreduced turnover rates in the jobs mostly held by the women.
Thecity relied on the Median Statistics to show the rates ofinequalities in the paychecks of men and females. The weekly salarydata from a hypothetical institution with 18 employees is arranged inorder where it depicts huge variations in the paychecks. Thedifference ranges from 290 dollars to 2000 dollars. To locate themedian of this distribution, we count the total number ofobservations (19), add an extra view and then divide it by two thus,obtaining ten. This value does not indicate the real value but theposition of the median. In our case, the median is 500.
Themedian of distribution can be derived by computing the averagecommonly referred as the mean. This value is calculated by adding upthe number of values and dividing it by the number of observations.In our hypothetical company, the mean would be 715 dollars which ishigher than the median we obtained. The average is perceived as thebouncing point of values and is greatly influenced by the highestsalary. The statisticians call the Median "the resistor”because any value does not control it on the extremes.
Theshape of distribution can hint at the relationship between the meanand the median. The mean and the midpoint are roughly the same insymmetric data. In a distribution that is skewed to the right, themean is larger than the median. If the distribution is skewed to theleft, the average becomes smaller than the center. The mean is pulledtowards the tail.
AgainstAll Odds: Inside Statistics – Annenberg Learner, video #4: Measuresof Center  https://www.learner.org/courses/againstallodds/unitpages/unit04.html