Practical Applications of Statistics

Practical Applications of Statistics

Statistics is a collection of procedures and principle for gaining and processing information in order to make decisions when faced with uncertainty. (Davis, Simon & Utts, 2002).

This paper will concentrate the on the practical application of the following statistical concepts Ð'- standard deviation, mean, mode, and median concepts, frequency polygon and sampling techniques.

Standard Deviation

The standard deviation method is one of the most commonly used statistical tools. It gives a precise measure of the amount of variation in any group of numbers. One practical use of standard deviation is to measure risk of investing in mutual funds or other investment products. It can also be used for a number of different purposes in investment decision-making. As a measure of volatility, standard deviation measures the tendency of data to be spread out.

When looking at the historic returns of a mutual fund, standard deviation can be used to measure the variation of expected return that has taken place in the past giving a sense of range of performance that can be expected given different probabilities of return for the future. According Harrell (1997),"When used to measure the volatility of the performance of a security or a portfolio of securities, standard deviation is generally calculated for monthly returns over a specific time period--frequently 36 months. And, because most people think about returns on an annual, not monthly, basis, the resulting number is then modified to produce an annualized standard deviation."

Mean, Mode, and Median

The mean of a list of numbers is the average of those numbers. Mean is calculated by adding all the numbers in the list and dividing by the number of numbers in the list.

Companies can use mean to calculate the average company salary as in the table below. The mean salary is higher than all but two salaries because of the salary of the manager of $60,000.

Table 1.0 Ð'- Employee Salaries

Employees Salaries

Secretary $12,000

Bookkeeper $19,000

Machinist, level 1 $15,000

Machinist, level 1 $15,000

Machinist, level 1 $15,000

Machinist, level 2 $18,000

Machinist, level 2 $18,000

Machine supervisor $22,000

Sales Representative $20,000

Sales Representative $20,000

Owner $60,000

Total $234,00

Mean or Average $21,273

Mode is the most frequent value. An advantage of mode is that it can be used for nonnumeric data. Mode can be used to describe the United States Senate by saying the mode sex of the senators is male and their race is Caucasian.

Median is the middle value of a list. If the list has an odd number of entries, the median is the middle entry in the list after sorting the list into increasing order. If the list has an even number of entries, the median is equal to the sum of the two middle entries, after sorting the numbers. A practical use of the median concept is to compute the mean weekly salary of a group of doctors.

Frequency Polygon

A frequency polygon is a graphical display of a frequency table. A practical use for frequency polygon would be to compute the percentage of student who received a certain test score. Frequency polygons can be based on the actual frequencies or relative frequencies.