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The mean is a commonly used measure of central tendency in statistics, representing the average value of a set of data. It is calculated by adding all the values in a data set and dividing by the total number of values. While the mean has several advantages, such as being easy to calculate and understand, it also has some disadvantages that should be considered.
One of the main advantages of using the mean is its simplicity. It can be easily calculated and understood by individuals with basic mathematical knowledge. Additionally, it takes into account all the values in a data set, making it a comprehensive measure of central tendency.
Another advantage of the mean is that it is not affected by extreme values, or outliers, in a data set. This makes it a more robust measure compared to other measures of central tendency, such as the median or mode.
However, there are also some disadvantages to using the mean. One major disadvantage is that it can be heavily influenced by extreme values, particularly in small data sets. This can result in a skewed representation of the data and may not accurately reflect the overall trend.
Another disadvantage of the mean is that it does not take into account the distribution of the data. In cases where the data is not normally distributed, the mean may not accurately represent the data and can lead to misleading conclusions.
In summary, the mean has both advantages and disadvantages in statistics. While it is a simple and robust measure of central tendency, it can also be affected by extreme values and may not accurately represent the data in certain cases. Therefore, it is important to consider the nature of the data and the potential limitations of the mean when using it in statistical analysis.
Advantages & Disadvantages of Using Mean in Statistics
The mean of a dataset represents the average value of the dataset.
It is calculated as:
Mean = Σxi / n
where:
- Σ: A symbol that means “sum”
- xi: The ith observation in a dataset
- n: The total number of observations in the dataset
There are two main advantages of using the mean to describe the “center” or “average” of a dataset:
Advantage #1: The mean uses all of the observations in a dataset in its calculation. In statistics, this is generally a good thing because we say we use all of the available information in a dataset.
Advantage #2: The mean is easy to calculate and interpret. The mean is the sum of all observations divided by the total number of observations. This is both easy to calculate (even by hand) and easy to interpret.
However, there are two potential disadvantages of using the mean to summarize a dataset:
Disadvantage #1: The mean is affected by outliers. If a dataset has an extreme outlier, this affects the mean and causes it to be an unreliable measure of the center of a dataset.
Disadvantage #2: The mean can be misleading with skewed datasets. When a dataset is skewed to the , the mean can be a misleading way to measure the center of a dataset.
The following examples illustrate these advantages and disadvantages in practice.
Example 1: The Advantages of Using the Mean
Suppose we have the following histogram that shows the salaries of residents in a particular city:
Since this distribution is mostly (if you split it down the middle, each half would look roughly equal) and there are no outliers, the mean is a useful way to describe the center of this dataset.
The mean turns out to be $63,000, which is located approximately in the center of the distribution:
In this particular example, we were able to use the two advantages of the mean:
Advantage #1: The mean uses all of the observations in a dataset in its calculation.
Since the distribution was mostly symmetrical and there were no extreme outliers, we were able to use every available salary to calculate the mean, which gave us a good idea of the “average” or “typical” salary in this particular city.
Advantage #2: The mean is easy to calculate and interpret. It’s easy to understand that the mean salary of $63,000 represents the “average” salary of an individual in this city.
While some individuals earn much more than this and some earn much less, this mean value gives us a good idea of a “typical” salary in this city.
Example 2: The Disadvantages of Using the Mean
Suppose we have a distribution of salaries that is right skewed and we decide to calculate both the mean and median salary:
The higher values on the tail end of the distribution pull the mean away from the center and towards the long tail.
In this example, the mean tells us that the typical individual earns about $47,000 per year while the median tells us that the typical individual only earns about $32,000 per year, which is much more representative of the typical individual.
In this example, the mean does a poor job of summarizing the “typical” or “average” value in this distribution since the distribution is skewed.
Or suppose we have another distribution that contains information about the square footage of houses on a certain street and we decide to calculate both the mean and median of the dataset:
The mean is influenced by a couple extremely large houses, which causes it to take on a much larger value.
This causes the mean square footage value to be misleading and a poor measure of the “typical” square footage of a house on this street.
Additional Resources
The following tutorials provide additional information about the mean and median in statistics: