## Mrs. Kim’s Annual Income for 15 years

## Explanation

Descriptive statistics, like the ones used to analyze data above, are used to describe data in a summarized manner. The mean as a measure of central tendency summarizes data in such a manner that it gives an average figure of the data. The mean is thus an important measure when one wants to have a summarized look of data to make quick judgments. For instance, the mean for the above data is $ 37731.5 meaning that Mrs. Kim had an annual real income of $ 37731.5 on average for the 15 years evaluated.

It is thus easy to conclude that even in the next ten-year period, Mrs. Kim’s real income will still be within this average. However, it is imperative to establish a marginal error level when using means to forecast future income to account for any adjustments that might take place. A person’s annual income can either increase or decrease based on the prevailing economic conditions.

Apart from the mean, the median is another important measure of central tendency. Median gives the score that appears in the middle of data if all the scores are arranged in numerical order. The median is also used to give a summarized description of data and is often associated with income. The median figure is usually taken as a quick average for the data. For instance, the median in the above data is $ 37853.88. It is thus easy to say that Mrs. Kim’s annual income is $ 37853.88 on average. Mean and median for data can either be the same or have a slight variation depending on the distribution of scores.

While mean and median are used to measure central tendency, standard deviation and variance are used to measure dispersion in any given data. They estimate the dispersion of scores about the mean. Standard deviation estimates how near or far the scores are from the mean. The standard deviation for the above data is 687.1971. Comparing this to the mean, it is clear that approximately 95% of scores in this data are within two standard deviations.

Mrs. Kim’s average annual real income is thus a true picture of her annual real income over this period. If standard deviation detects that the outlier scores are far from the mean, then it is inappropriate to use the sample mean to summarize the data as it will be exaggerated. The variance, which is the square of standard deviation measures dispersion within scores. It estimates how far apart the scores are from each other.

It is a probability measure of how far apart a measure of data in the same phenomena will be distributed in the future. For instance, we can use variance in the above data to estimate how Mrs. Kim’s annual real salary will be distributed in the next ten years. From the variance above, I can assume that Mrs. Kim’s annual salary will be distributed in a manner almost similar to the current data.