HM is appropriate in situations where the reciprocals of values are more useful. HM is used when we want to determine the average sample size of a number of groups, each of which has a different sample size. If all the values in a data set are the same, then all the three means arithmetic mean, GM and HM will be identical.
As the variability in the data increases, the difference among these means also increases. Arithmetic mean is always greater than the GM, which in turn is always greater than the HM. The other measures of central tendency median and mode and the guidelines for selecting the appropriate measure of central tendency will be dealt with in the subsequent issue. Source of Support: Nil. Conflict of Interest: None declared.
National Center for Biotechnology Information , U. Journal List J Pharmacol Pharmacother v. J Pharmacol Pharmacother. Author information Copyright and License information Disclaimer. Assistant Editor, Journal of Pharmacology and Pharmacotherapeutics. E-mail: moc. This is an open-access article distributed under the terms of the Creative Commons Attribution-Noncommercial-Share Alike 3. This article has been cited by other articles in PMC. MEAN Mean is the most commonly used measure of central tendency.
Table 1 Standard statistical notations. Open in a separate window. Weighted mean Weighted mean is calculated when certain values in a data set are more important than the others. Geometric Mean It is defined as the arithmetic mean of the values taken on a log scale.
Harmonic mean It is the reciprocal of the arithmetic mean of the observations. Manikandan S. Frequency distribution. Unless data points are known mistakes, one should not remove them from the data set! One should keep the extreme points and use more resistant measures. For example, use the sample median to estimate the population median. We will discuss methods using the median in Lesson What happens to the mean and median if we add or multiply each observation in a data set by a constant?
What effect does this have on the mean and the median? The result of adding a constant to each value has the intended effect of altering the mean and median by the constant. For example, if in the above example where we have 10 aptitude scores, if 5 was added to each score the mean of this new data set would be Similarly, if each observed data value was multiplied by a constant, the new mean and median would change by a factor of this constant.
Returning to the 10 aptitude scores, if all of the original scores were doubled, the then the new mean and new median would be double the original mean and median. As we will learn shortly, the effect is not the same on the variance! Why would you want to know this?
One reason, especially for those moving onward to more applied statistics e. For many applied statistical methods, a required assumption is that the data is normal, or very near bell-shaped. When the data is not normal, statisticians will transform the data using numerous techniques e. We just need to remember the original data was transformed!! The shape of the data helps us to determine the most appropriate measure of central tendency. The three most important descriptions of shape are Symmetric, Left-skewed, and Right-skewed.
Skewness is a measure of the degree of asymmetry of the distribution. Salary distributions are almost always right-skewed, with a few people that make the most money. To illustrate this, consider your favorite sports team or even the company for which you work. This will produce a shape that is skewed to the right.
Knowing this can be a useful aid in negotiating a higher salary. That is, they are offering you the average salary for someone with your particular skill set e.
But is this average the mode, median, or mean? The company — for whom business is business! Since salaries tend to be skewed to the right, the offer will most likely reflect the mode or median. Once you have these averages, you can begin to negotiate toward the highest number. The most commonly used measure of central tendency is the mean. To calculate the mean of a dataset, you simply add up all of the individual values and divide by the total number of values.
For example, suppose we have the following dataset that shows the number of home runs hit by 10 baseball players on the same team in one season:. The mean number of home runs hit per player can be calculated as:. The median is the middle value in a dataset. You can find the median by arranging all the individual values in a dataset from smallest to largest and finding the middle value. If there are an odd number of values, the median is the middle value. If there are an even number of values, the median is the average of the two middle values.
For example, to find the median number of home runs hit by the 10 baseball players in the previous example we can arrange the players in order from least to greatest number of home runs hit:.
Since we have an even number of values, the median is simply the average of the two middle values: In this case, since we have an odd number of values the median is simply the middle value: The mode is the value that occurs most often in a dataset.
A dataset can have no mode if no value repeats , one mode, or multiple modes. The following dataset has one mode: This is the value that occurs most frequently. The following dataset has three modes: 8, 15, These are the values that occur most frequently. The mode can be a particularly helpful measure of central tendency when working with categorical data because it tells us which category occurs most frequently.
The mode , or the response that occurred most frequently, was blue. The mode can also be used for numerical data, like we saw in the above example with baseball players. For example, suppose we want to know the typical number of home runs hit by a baseball player on this team:. The mode of this dataset is 8, 15, and 19, since these are the values that occur most frequently.
A better measure of central tendency would be the median 15 or the mean also 15 in this case. The mode is also a poor measure of central tendency when it happens to be a number that is far away from the rest of the values.
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