The Use of Normal Distribution Statistics in Business (Essay Sample)

The Use of Normal Distribution Statistics in Business
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The Use of Normal Distribution Statistics in Business
Introduction
Statistics plays a huge part in business decisions. Any business has to be sharp and accurate when making its decisions. The business has to have a feel for demand of the company's products. It should therefore have the ability to identify what proportion to produce or the level of services that it will sell. These volumes of sale also have to be accurately estimated. Statistics help businesses align production according to demands in the market. Using business statistics will enable the quality and amount of the products to be established in a scientific manner and therefore help to save on cost. This is in addition to determining the costs of services rendered to the business by input factors such as labor. Thus, business managers can utilize statistical information to make business decisions. This paper discusses the various concepts used in calculating normal distribution statistics and their application in business practices.
Discussion
A normal distribution is a distribution of a set of data that is bell-shaped and symmetrical. It is also often called “the bell-shaped curve because of its shape” (Black, 2012). The curve is concentrated at the center and decreases on either side indicating that the data has fewer tendencies to produce outliers. The outliers are the extreme ends of the set.
At the peak of the normal distribution curve falls the mean, mode and median. These three measures will have the same number if the normal distribution is perfect. There are two equal halves on each side of the middle of the distribution and the height and the width of the bell is determined by standard deviation. The standard normal distribution usually has a mean of 0.0 and a standard deviation of 1.0.
Mean
The mean is the most popular measure of central tendancy and is most often used with continuous data. It is equal to the total value of all the set of data divided by the number value, the amount of values, which are in the data set. Therefore, if you have values x1, x2, x3…xn and you have n values in the data set, the sample mean which is denoted by
, is;


This formula can be written in a completely different way by using a Greek capitol letter, written as
and pronounced as "sigma", which is used to mean "sum of...” These symbol indicates that the summation of the whole data set x is calculated for the use in the calculation of the mean of the data set.


The mean minimizes errors in the prediction of the values of the data set and also includes every value of the data set as a part of this calculation.
The mean is the only central tendency measure in which the sum of the deviations of each value from the mean is always zero. Businesses can apply this concept to determine the price at which it can break even in its operations- balancing expenditure and sales. Similarly, the mean is used to determine the most common value. For instance, a business can use the mean to determine or estimate market rates, such as the average pay of a CEO in a given industry. This is achieved by taking the salaries of the CEOs of different companies and calculating their average. In this way, a business will be able to determine how much it should pay its own chief executive officers. In this regard, the mean is useful in business practices because it minimizes the margin of error when predicting the other values in the data set.
However, the mean tends to be biased in a data set with outliers- values that are either too large or too small compared to the rest of the data. Thus, it gives a false impression of the overall central tendency. For instance, the mean of employees in an organization may not accurately capture the disparity between junior employees and executive officers. For instance, these figures exhibit a big disparity in the salaries of an organization.
StaffCleanerCookMessengerJunior ClerkSecretary Junior ManagerSenior Manager CEOSalary in $5k7k10k14k17k25k40k70KThe mean salary for this staff is $23.5k. However, scrutinizing the data shows that the mean value may not be the best way to accurately gauge the typical wage of a worker. This is because the salary of most workers is below the 20k mark. In this light, the CEO’s salary of $70k is an outlier in the data set because it is way far above the mean wage. This is the case in skewed data sets, whereby there is a large difference between the highest value and other values. In a normally distributed data, however, the mean, median, and mode tend to be identical, making these variable relevant measures of central tendency. As will be discussed later, the use of the median and inter-quartile range measures help in removing these outliers as a means of determining an accurate measure of central tendency. Nevertheless, normal distribution statistics represent a perfect model of assessing the fairness of business practices, such as measuring how far a business’s wage structure deviates from the average market rates.
Median
The median is a measure of central tendency that indicate the middle score of a data. For a set to be calculated the set of data should be arranged in the order of the set’s magnitude, that is from the smallest to the highest in ascending order or from the highest to the lowest in descending order. The median is a reliable measure of central tendency because it is not affected much by the outliers (extreme values) and/or by skewed data. This implies that regardless of how much the data is varied or how far the values deviate from the mean, the median will be the same. To put it into perspective, let us use the data below to determine the median:
50354433 35265545674872We will have to first rearrange this data into an order of magnitude that is, either in ascending order or descending order. In this case we arrange the set ascending order- from the lowest value to the highest.
2633353544454850556772
Our median is the middle mark, 45. For an even number of scores, you get the two middle values and average their result. The median is preferred over mean when data is skewed because it is not influenced by outliers.
Mode
This measure of central tendency indicates the most frequent score in a set of data. It is that value in the data that has appeared in the data set the most number of times. It is normally used for categorical data in knowing the most common category. This is illustrated below:


From the above set of data, the most used means of transport is the bus. Therefore, for these sets of data the bus is the mode. However, when the data contains more than to values sharing the highest frequency, it becomes problematic to use the mode as a measure of central tendency. For this reason, the mode is not used to analyze continuous data. In a business context, the mode is used to determine the most popular trend. This is important in decision making as it helps a business realign its practices to reflect market behaviors. For instance, a company may decide to pay its lowest earning worker $10k if that is what other businesses in the same industry pay their workers.
Application of Mean, Mode and Median
In preference to the median, the mode can be used to measure location of popular items when required for example number of defects in a sample. Mode can also be used to analyze prices paid by the majority of customers as well as the group of customers that are valuable to the business.
The mean would be preferred over any other average in distributions that are symmetric and where further statistical calculations are needed. For example, the number of items manufactured daily in a large assembly line, or a firm orders per month. The mean can also give average cost and form a basis for future cost estimates. Prediction of future estimates would be essential in making budgets and therefore help a firm focus its effort to a predetermined outcome. In addition, prediction enables firms to make proforma balance sheets which are very vital in predicting future cash requirements. Thus, the mean can help a business make decisions about future expenditures by making predictions on the basis of current trends as reflected by the mean.
The median can be used in a skewed distribution or where data is costly to measure. For example, the median can be used to determine the employee’s salaries, sales turnover for a large group of companies. However, the mean is preferred over the median and mode in normal distribution statistics because it takes into account all the values in a given data set. This is unlike the mode and mean, which mainly emphasize on the middle values and is not affected by a change of the other scores.
Standard deviation
Standard deviation shows the variation from expected or average value of data. Standard deviation is the square root of the variance and is normally expressed in the same data units. In a standard normal distribution, the standard deviation is equal to one. Standard deviation is calculated as


In a bell curve, about 68% of the area under the curve falls within 1 standard deviation, 95% within 2 standard deviations and 99.7% falls within 3 standard deviations. Standard deviation of a sample will show the variability of the population from which a sample is drawn.
In a business scenario, the standard deviation can be used to ascertain how and to what extend the business results vary from the average. If the average outcome was the projected or the budgeted output, then standard deviation can be used to determine by how much the real output was varied from what was projected. Standard deviation is also very useful in determining portfolio risk. Portfolio risk is the risk assoc...