simple harmonic mean

Harmonic mean is an alternate form of average that focuses on the mid-range numbers of a given set. It can be a powerful tool in calculations that involve the comparison of extremely different values. Whereas the traditional mean of a set of numbers equals the sum of those numbers divided by their quantity, the harmonic mean uses the reciprocal number of the set and figures in the sum of its reciprocals. While it is a relatively simple process to determine the harmonic mean, it can be applied to a number of information-comparison scenarios.

The harmonic mean value of a set can help account for the outlier numbers that skew the standard mean. Imagine a set containing the numbers from 1 to 10. The traditional mean of the set is 5.5, but if the set consisting of numbers 1, 6 and 10, the harmonic mean is (1/1 + 1/6 + 1/10 = 5.9), which isolates the midpoint of the set and eliminates the higher and lower values. This is beneficial when dealing with populations with a large discrepancy among individuals. For example, if a group of 7 employees have salaries of $20,000, $30,000, $60,000, $70,000, $75,000, $90,000 and $100,000, the traditional mean salary is $64,285.71, which gives the impression that the majority of employees are making close to the average. The harmonic mean, however, comes to $55,555.55, which more accurately reflects the extreme number of employees on the lower and upper ends of the range.

Another practical application of harmonic mean involves calculating the speed of a driver traveling at different speeds over a set period of time. If a driver travels 10 miles in 10 minutes, 10 miles in 20 minutes, 10 miles in 30 minutes and 10 miles in 40 minutes, the traditional mean comes to 25 mph, which reflects the total miles over total minutes. The harmonic mean, however, comes to 17.64 mph, which takes into consideration that two thirds of the time was spent going slower than 25 mph.

Harmonic mean can also be used in population measurement. If a certain fish population consists of 7 fish that weigh 200, 500, 1,300, 2,000, 2,500, 3,000 and 3,500, the traditional mean weight is 2,471 and indicates that the majority of fish in the population weigh about 2,400 grams. However, the harmonic mean of 980 gives more insight into the fact that the majority of the population is nearer to the lower end of the range.

Harmonic mean can be a useful tool in many applications. It offers a different perspective on the midpoint of a set and can bring to light dramatic discrepancies that are often unleashed by the traditional mean.

Arithmetic mean or the simple average, is a statistical technique that is used to calculate a data set from the sum of its numbers divide by the total count of numbers in the data set. It is used to provide one of the various measures of central tendency of a data-set or population. The Arithmetic mean is the most common type of average calculated, which can return a very specific mean value which is determined through calculation, for example the mean of 2, 3 and 5 will be 3.67.

In mathematics, the arithmetic mean is used to describe the mean or the average value of a data set. This is calculated by adding all of the values together in the data set, then dividing this total by the total count of numbers in the data set. The averaging process of the arithmetic mean produces a value which is called the mean of the data set and this value is used as a reference point in various statistical calculations.

The arithmetic mean is often used in descriptive statistics. It can be used to make estimates about a population when sample size is small, but it is always limited due to sample size. Additionally, it can be used to calculate the range of a data set and its deviation from the mean average. It is also an important metric in calculating risk, as it measures what can be expected to happen on average.

The arithmetic mean is very useful in day to day life. It can be used to measure academic performance, pricing, accounting, investments and more. It is also useful when assessing large population of people where sample size may be large, such as national census data sets.

In conclusion, the arithmetic mean is an important statistical technique that measures central tendency and can be used in many situations, both scientifically and in everyday life. It is one of the simplest and most effective data analysis techniques available.