“Measures of central tendency (averages) are statistical constants which enable us to figure out in a single effort the significance of the whole.” (Prof Bowley) The main objectives of measure of central tendency are:
- To reduce data in a single value.
- To make easy comparisons between data.
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There are different types of averages; each has its own business applications.
- Arithmetic Mean
- Geometric Mean
- Harmonic Mean
Most important measure of location is the mean or average value, for a variable. The mean provides a measure of central location for the data. If the data are for a sample, the mean is denoted by; if the data are for a population, the mean is denoted by the Greek letter μ. (David R. Anderson et al)
Business Applications of Mean
The arithmetic mean is considered a deal average. It is frequently used in all the aspects of business i.e. number of items produced per day on a large assembly line, number of orders received per month for a firm. further In economic analysis arithmetic mean is used extensively to calculate average production, average wage, average cost, per capital income exports, imports, consumption, prices, etc. (www.publishyourarticles.net)
Say we want to find the average annual salary of all secretaries. We believe we can do this on the basis of our knowledge of annual salaries of 6 particular secretaries, who each earn $.10400, $34000, $14000, $25800 respectively.
Our result is a sample mean because we are interested in finding the mean annual income of all secretaries on the basis of the annual income of a smaller sample consisting of only 6 secretaries. (Cheng F. Lee et al, 1993)
The median is another measure of central location. The median is the value in the middle when the data are arranged in ascending order. With an odd number of observations, the median is the middle value. An even number of observations has no single middle value. In this case, we follow convention and define the median as the average of the values for the middle two observations. (David R. Anderson et al)
Business Applications of Median
Median is positional measures of central tendency. The median salary gives a value close to the average salary commonly paid, without taking the extreme values into consideration. There are mainly used in the qualitative cases like honesty, intelligence, ability, etc. These are also suitable for the problems of distribution of income, wealth, investment, etc. (www.publishyourarticles.net)
The U.S. Census Bureau finds the median household income. According to the U.S. Census Bureau, "median household income" is defined as "the amount which divides the income distribution into two equal groups, half having income above that amount, and half having income below that amount." (www.ehow.com) 1.3 Mode
The mode is defined as the element that appears most frequently in a given set of elements. The mode can also be defined as the element with the largest frequency in a given data set. (www.wyzant.com) 1.3.2 Business Applications of Mode
The mode is the most important when an analysis is looking for what happens most often. In analyzing prices, most of the sales occur at a particular list price or possibly at a reduced, sale price. While there may have been sales at other prices, very few customers will have paid an average or a mean price. Those values are therefore less important when setting pricing in terms of what most customers paid. (www.publishyourarticles.net)
Mode is used to calculate the 'modal size of a collar', 'modal size of shoe', or 'modal size of ready-made garments' etc.The mode may be beneficial for a manager of a shoe store. For example, you would not see size 17 shoes stocked on the floor. Why? Because very few people have a size 17 shoe size. Therefore, store managers may look at data and determine which shoe size is sold the most. Managers would want to stock the floor with the best selling shoe size. (www.ehow.com)
Geometric mean is well defined only for sets of positive real numbers. This is calculated by multiplying all the numbers (call the number of numbers n), and taking the nth root of the total. (ww.easycalculation.com)
Business Applications of Geometric Mean
Geometric Mean is used in the construction of index number. The averages of proportions, percentages and compound rates are computed by geometric mean. The growth of population is measured in it as population increases in geometric progression.
Harmonic mean is used to calculate the average of a set of numbers. Here the number of elements will be averaged and divided by the sum of the reciprocals of the elements. The Harmonic mean is always the lowest mean. (ww.easycalculation.com)
Business Applications of Harmonic Mean
Harmonic mean is applied in the problems where small items must get more relative importance than the large ones. It is useful in cases where time, speed, values given in quantities, rate and prices are involved. But in practice, it has little applicability.
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