History and Definition of Frequency Analysis
The study of quantitatively describing the characteristics of a set of data is called descriptive statistics. Frequency Analysis is a part of descriptive statistics. In statistics, frequency is the number of times an event occurs. Frequency Analysis is an important area of statistics that deals with the number of occurrences (frequency) and analyzes measures of central tendency, dispersion, percentiles, etc.
Frequency Analysis usually deals with three types of measures –
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Measures of Central Tendency
It is a single measure that tries to describe the set of data through a value that represents the central position within that data set. Most popular measures of central tendency used for frequency analysis are Mean, Median and Mode. While the mean is the average value of the data set, the median is the middle observation (observation which has an equal number of values lying above and below it) in the data set. Mode is the value that occurs the most number of times in a data set.
While Mean has been calculated by mathematicians and astrologers since ages, Median was first introduced by Edward Wright in his book on navigation in 1599; and Mode originated in 1895 by Karl Pearson's efforts.
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Measures of Dispersion
These reflect the spread or variability of data within a data set. Most popular measures of dispersion used for frequency analysis are Standard Deviation, Variance and Range.
While Standard Deviation had been around for a long time and had been used by others with different names (like 'mean error' by Gauss); Karl Pearson first used the term Standard Deviation in 1894. Variance was first used by Ronald Fisher in 1918.
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Percentile Values
A percentile value shows what percent of values in a data set fall below a certain percent. Frequency Analysis commonly uses percentile values like Quartiles, Deciles, Percentiles, etc. While the 10th percentile value shows that 10% of the observations fall below it in a data set, it is also called the 1st Decile (where the data set is divided into 10 Deciles at intervals of 10% each). Similarly the 25th, 50th and 75th percentiles are also called the 1st, 2nd and 3rd Quartile respectively (where the data set is divided into 4 Quartiles at intervals of 25% each).
Illustration of Frequency Analysis
Say, an organization is looking to restructure employee remuneration and salary structure. It can collect employees' salary data across hierarchies and locations. Frequency Analysis can be conducted to find out mean, median, mode salaries and the standard deviation in salaries across levels and in different departments. The frequency analysis will aptly describe the data set and provide a fair idea of what most employees are earning, and how widely dispersed their salaries are. This would supply the snapshots required for a detailed analysis. On this basis, the compensation restructuring can be modeled and executed to improve employee satisfaction and increase productivity levels.
Practical Application of Frequency Analysis
Used together, these tools of frequency analysis are extremely important for analysis and interpretation of any data at a glance. Almost every sphere from scientific research to medical, climatic and geological studies, economic and policy decisions; business research and reporting use various forms of frequency analysis.
Say, a product company is studying consumer demographics of a region. It will use frequency analysis tools to get an estimate of consumer's average age, average disposable income, income variance in the region, average monthly spending, median monthly spending, average annual spend on a particular category of product, its standard deviation and so on. These basic statistics will provide extremely useful information to the company when deciding upon its marketing, positioning, pricing and distribution strategies.