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# Responding to discussion 300 words each

The measures of central tendency has three common components with include the mean, the median, and the mode. With using the three common measures of central tendency, a statistical measurement of a grouping or data set to obtain a value that represents the subject as a single value. The first component is the mean which can be considered the most powerful and commonly used measure of central tendency. With using the mean, a representative sample mean is identified by using the x bar symbol and a representative population sample is identified by mu (μ). A mean can be considered an average since the values presented are added up and divided by the number of input values. The second component withing the measures of central tendencies is the median. The median is center value when the values are placed in numerical order. The third component withing the measures of central tendencies is the mode. The mode is determined by selecting a representative sample and the value that most commonly appears is considered the mode (South University Online, 2019) (Zach, 2018).

These measures differ on the ways or methods to which they are applied from the data being analyzed. With the use of the mean, the average of the data sample will be determined. The median will find the central value of the data set when the values are placed in numerical order but may not be the actual average value. With the median of an odd number sample size, the average of the two central values is the median value and with an even sample size, the median is the central value. Finally with the mode, this is looking for repetitive values which occur within the representative sample. It is possible that there may not be any repetitive values resulting in no mode (South University Online, 2019) (Zach, 2018). The three components are the same since they all need a representative sample value to determine the objective outcome.

The measures of central tendency could be used by leaders, managers, or individuals to find the best approach to the outcome that desired. An example of this would be finding a faster way to navigate a process if using the mode method and a time period for delays reoccurs, an approach could be determined to circumvent that specific delay.

The various measures of dispersion are the standard deviation, range, and interquartile range (Manikandan, 2011). Standard deviation is the measure of dispersion that is the most commonly used out of the three concepts. The limitations of the standard deviation are dependent on the size of the sample and sigma level (standard deviation ±) percentage from the mean along with the data needing to be skewed (symmetrical bell curve) for it to be used (Manikandan, 2011). A limitation of range would be that the outliers (abnormal value) from the data set are not used. A limitation of interquartile range is that with a vast sample size spacing, the calculations are not able to be conformed a projected use (Manikandan, 2011).

These measures tell leaders, managers, or researchers’ various outcomes on sample or population data and could provide guidance to determining a method of approach in finding solutions to desired research, improvements to a process or the reasoning behind negative to marginal performance or even positive performance from the provided data set.

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A measure of central tendency is a value that attempts to describe a set of data by identifying the central position with that set of data (n.d.). The most common measures of central tendency are Mean, Mode, and Median. The Mean is described as the average of the data. This is usually described with arithmetic. If you had a set of numbers and wanted to find the Mean, you would add all of the numbers and then divide the sum by the amount of numbers collected. The Median, of course, is the middle score of the data that is arranged in order of magnitude (from largest to smallest or vice-versa). If you have an odd number of numbers in your data, the Median would be the middle number. If you have an even number, the Median would be the middle exactly. The mode is the most frequent score in data set. So, if you have a number set like 3, 4, 6, 6, 5, 8, 3, 3, 9. The Mode is the number that show up the most often. In this case the Mode would be 3.

These measures differ in the outcomes of the data set. They are the same in that they all use numbers and arithmetic to come to a conclusion.

The information that these measures give us could be used in a sales plan. If you gather data to set up a sales plan for a company. Take for instance, setting up a sales plan for a daily sale at Arctic Circle (where I was once an Assistant Manager), you look back to last years sales for the same date. You have to figure in the day of the week difference. You figure in the amount of people you have working at each hour of the day you are open. Then you factor in the weather and any outside events that might happen in your area. Then you divide the total expected sales by the number of employees to see if you need to let some people go early or keep them later.

In statistics, the measures of dispersion help to interpret the variability of data i.e. to know how much homogeneous of heterogeneous the data is (Admin, 2021). There are two main types of measures of dispersion. Absolute Measure of Dispersion and Relative Measure of Dispersion. With Absolute Measures of Dispersion, there are different types. There is Range, Variance, Standard Deviation, Quartiles and Quartile Deviation, and Mean and Mean Deviation. Common relative dispersion methods include Co-efficient of Range, Co-efficient of variation, Co-efficient of Standard Deviation, Co-efficient of Quartile Deviation, and Co-efficient of Mean Deviation.

The use of these measures is to find the Variance (difference) and likeness of the data collected and how it would help you find good information for your research. Some of the limitations of dispersion measures are that they may be misinterpreted. They may give inappropriate results. They may give a value of variation, which may not be practically found with the items of the series (2015).

These measures can tell a manager or leader the amount of work that is necessary to meet the sales plan and not exceed the amount of payout for employee pay, overhead, and resources.

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