When to Use Mean vs Median – Things You Need To Know

When to Use Mean vs Median

Want to know when to use mean vs median? Then you are at the right place. In statistics, the mean and median are two measures of central tendency that provide important insights into numerical data. The mean is the average of a dataset, while the median is the middle value of a dataset. 

In this blog, we will discuss the applications of mean and median in different fields. The choice between using mean or median depends on the data’s nature and the analysis’s purpose.

What is Mean?

In statistics, the mean is a measure of central tendency representing the average value of a numerical data set. It is calculated by adding up all the values in the dataset and then dividing the total by the number of observations. The mean is also known as the arithmetic mean or the average.

The Formula For Calculating The Mean Is:

Mean = (sum of all observations) / (number of observations)

For example, if we have the following dataset of test scores:

80, 85, 90, 95, 100

The mean would be calculated as:

mean = (80 + 85 + 90 + 95 + 100) / 5

mean = 450 / 5

mean = 90

Therefore, the mean test score is 90.

What Is The Use Of Mean?

The mean is a commonly used statistical measure that is useful in many different areas. Here are some examples of the uses of mean:

  1. The measure of central tendency: The mean is a measure of central tendency that provides an overall summary of the dataset. It represents the “typical” value of the dataset.
  2. Comparing different datasets: The mean can be used to compare different datasets. For example, the mean income of two different countries can be compared to determine which country has a higher income level.
  3. Prediction: The mean can be used to make predictions about future events. For example, if the average number of sales per month is known, the mean can be used to predict the number of sales for the next month.
  4. Quality control: The mean can be used in quality control to monitor the consistency of a process. If the mean of a process changes significantly, it may indicate a problem that needs to be addressed.
  5. Statistical inference: The mean is a key component in many statistical tests and models. It is used to estimate parameters and test hypotheses about the population from which the data was collected.

Overall, the mean is a useful statistical measure that provides important insights into numerical data. It is widely used in research, business, and other fields where numerical data is analyzed.

What is the Median?

In statistics, the median is a measure of central tendency representing a dataset’s middle value when the values are arranged in order from smallest to largest (or largest to smallest).

The median is the middle value if the dataset has an odd number of values. If the dataset has an even number of values, the median is the average of the two middle values.

For example, if we have the following dataset of test scores:

80, 85, 90, 95, 100

The median would be calculated by arranging the data in order:

80, 85, 90, 95, 100

Since there is an odd number of values, the median is the middle value, 90.

Another example if we have the following dataset of salaries:

$40,000, $45,000, $50,000, $55,000

The median would be calculated by arranging the data in order:

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$40,000, $45,000, $50,000, $55,000

Since there is an even number of values, the median is the average of the two middle values: ($45,000 + $50,000) / 2 = $47,500.

The median is a useful measure of central tendency when the data is skewed or has extreme values, as it is less sensitive to outliers than the mean. Therefore, it is often used in situations where extreme values may greatly impact the mean.

What Is The Use Of Median?

The median is a commonly used statistical measure useful in many different areas. Here are some examples of the uses of median:

  1. The measure of central tendency: The median is a measure of central tendency that provides an alternative to the mean. It represents the middle value of the dataset and is useful when the data is skewed or has extreme values.
  2. Comparing different datasets: The median can be used to compare different datasets. For example, the median income of two countries can be compared to determine which country has a higher income level, even if the income distribution is skewed.
  3. Outlier detection: The median is useful in identifying outliers in a dataset. Outliers are data points significantly different from the rest of the data. Since the median is less sensitive to outliers than the mean, it can be used to identify potentially problematic values.
  4. Survival analysis: The median is commonly used to estimate the time of an event, such as the time until a patient dies or the time until a machine fails.
  5. Skewed data: The median is a better measure of central tendency when the data is skewed, as extreme values do not influence it in the same way as the mean. For example, the median is a useful measure of central tendency for income data, which often has a skewed distribution.

Overall, the median is a useful statistical measure that provides important insights into numerical data. It is widely used in research, business, and other fields where numerical data is analyzed.

Applications of Mean

1. Measure of central tendency

The mean is a commonly used measure of central tendency representing a dataset’s average value. It provides a summary of the dataset that can be used to compare different datasets or to monitor changes over time. For example, if we have a dataset of daily temperatures over a month, we can calculate the mean temperature to get an idea of the average temperature over the month.

2. Quality control

The mean is also useful in quality control to monitor the consistency of a process. If the mean of a process changes significantly, it may indicate a problem that needs to be addressed. For example, if a manufacturer produces a certain product and the mean weight of the product changes significantly, it may indicate a problem with the manufacturing process.

3. Statistical inference

The mean is a key component in many statistical tests and models. It is used to estimate parameters and test hypotheses about the population from which the data was collected. For example, suppose we have a dataset of test scores and want to compare the scores of two groups. In that case, we can use a statistical test that compares the means of the two groups to determine if there is a significant difference.

4. Prediction

The mean can also be used to make predictions about future events. For example, if the average number of sales per month is known, the mean can be used to predict the number of sales for the next month. This can be useful in business planning and forecasting.

Applications of Median

1. The measure of central tendency

The median is also a measure of central tendency that provides an alternative to the mean. It represents the middle value of a dataset and is useful when the data is skewed or has extreme values. For example, we have a dataset of salaries and a few individuals have extremely high salaries. In that case, the median may be a more appropriate measure of central tendency than the mean.

2. Comparing different datasets

The median can also be used to compare different datasets. For example, the median income of two countries can be compared to determine which country has a higher income level, even if the income distribution is skewed.

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3. Outlier detection

The median is useful in identifying outliers in a dataset. Outliers are data points that are significantly different from the rest of the data. Since the median is less sensitive to outliers than the mean, it can be used to identify potentially problematic values. For example, if we have a dataset of test scores and a few individuals have extremely high or low scores, the median may be a more appropriate measure of central tendency than the mean.

4. Survival analysis

The median is commonly used in survival analysis to estimate the time of an event, such as when a patient dies or when a machine fails. For example, if we have a dataset of the time until a machine fails, we can calculate the median time of failure to understand how long the machine is expected to last.

5. Skewed data

The median is a better measure of central tendency when the data is skewed, as extreme values do not influence it in the same way as the mean. For example, the median is a useful measure of central tendency for income data, which often has a skewed distribution.

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When to Use Mean vs Median – Things You Need To Know

The mean and median are two important statistics for analyzing data sets. They both have their own strengths and weaknesses.

The mean is a simple arithmetic average of all the numbers in a set. The median, on the other hand, is a positional average that highlights the middle number of an array set.

1. Skewed Distributions

When a data set has a skewed distribution, the relationship between mean vs median changes. The longer tail in a skewed distribution tends to pull the mean away from the most common values.

The opposite happens in a right-skewed distribution. The mean is greater than the median in a right-skewed distribution.

Skewed distributions are more common than normal distributions. For example, the average age of death is skewed to the left as most people die at an older age.

A distribution with a positive skew has a long tail on the left side of the number line, whereas a negative skew has a short tail on the right side.

These asymmetrical distributions may not be a good fit for statistical tests. This is because the long tail in a skewed data set can lead to inaccurate results from these tests. This is especially true in the case of start-up effects. Consequently, more sophisticated statistical techniques are required to analyze these data sets.

2. Outliers

Outliers are values that differ greatly from the others within a data set. They may indicate variabilities in measurement, experimental errors, or a novel situation that requires special attention.

They also can affect the use of mean vs median. For example, a value that is far out of the center of a data set can cause a mean value to be significantly higher than it should be.

The effect is most noticeable when the outlier has a large impact on the data. For instance, a value that is a million dollars or more above the average income of college students can have a significant effect on the mean.

One method for detecting outliers is to plot the data as a box plot. This can be done with Excel or using a python module such as Plotly.

3. Intuitiveness

Intuition is the ability to trust patterns, connections, and hidden meanings. It is an inner voice or sixth sense that helps people make decisions. Intuitive people are often more successful than their less intuitive counterparts.

For example, an intuitive person will be able to spot when something is right or wrong. They are also able to see the big picture and connect things.

But intuitiveness can be hard to design for because it differs between different individuals. It depends on cultural and social norms, personal experiences, and more.

This is why it is important to understand your target audience and how they will use your product. You can then take a nuanced approach to design intuitiveness for them.

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4. Robustness

Robustness testing is a type of software quality assurance that tests the system’s ability to handle exceptional inputs and harsh environmental conditions. It helps find those corner cases that can cause a system to crash.

Robust statistics are resistant to errors that result from deviations from assumptions, such as normality and heteroscedasticity. They also resist outliers, which can invalidate ordinary least squares (OLS) results.

Examples of robust statistics include the median, mode, and trimmed mean. They all resist outliers and are less susceptible to errors than other statistical formulas.

In terms of anomaly detection, robustness testing can help you identify and address bugs earlier in the development process. This can save you time and money by reducing the cost of rework or redesign later in the product’s life cycle.

5. Countable data

A countable data set is a data array containing values from smallest to largest. The median is the middle number in a countable data set that separates the upper and lower sets.

The median is usually used with countable data sets with even cardinality (meaning all of the numbers in the array are even). When a countable data array has odd cardinality, the mean must be calculated for the set first.

The mean is a powerful measure of central tendency, but outliers can skew it. Therefore, the median is better when your data is skewed or has many outliers.

6. Noncountable data

The mean and median are two of the most common measures of central tendency. They are calculated by adding all the values in a set together and then dividing that total by the number of values.

They are also useful for finding the middle value of a set of numbers. However, they are different in several important ways.

For one, the mean is easily skewed by large outliers. This means that it doesn’t consider the broader range of values in a dataset, making it less useful for determining trends among a data set.

On the other hand, the median is much less sensitive to outliers. This means that it’s a better choice for calculating the center of a dataset when the distribution is symmetrical and there are no outliers. It can also help provide a more intuitive sense of a “typical” value, which can be helpful when evaluating a dataset.

7. Normal distribution

A normal distribution is a type of probability distribution symmetric around its mean. This means that most of the data is clustered around the mean, while data become less frequent as you move away from the mean.

The normal distribution is a widely used probability distribution and is the key idea behind the central limit theorem, which states that averages calculated from independent, identically distributed random variables tend to form approximately normal distributions.

This makes the normal distribution a common tool for comparing groups and estimating populations using samples.

The probability density function of a normal distribution is f(x)=m (mu) dx, where m is the mean and s is the standard deviation. The standard deviation controls how to spread out your data is, which affects how tall the normal distribution will be.

Some General Guidelines: When to Use Mean vs Median

Here are some general guidelines to help you decide when to use mean vs median:

1. Mean

Use means when the data is normally distributed and there are no outliers. The mean is a good measure of central tendency when the data is evenly distributed around the average. For example, the mean is useful when calculating the average salary of employees in a company.

2. Median

Use the median when the data is not normally distributed or there are outliers. The median is a good measure of central tendency when the data is skewed or has extreme values. For example, the median is useful when calculating the typical income of households, where a few high earners may skew the average income.

Conclusion

This is the end of this post which is about when to use mean vs median. On the other hand, mean and median are two important measures of central tendency that provide important insights into numerical data. The mean is useful in many different applications, including quality control, statistical inference, and prediction. The median is also useful in many

Understanding the data’s characteristics and the distribution’s nature is important in selecting the appropriate measure of central tendency. By doing so, we can accurately describe and interpret the data, providing valuable insights for decision-making and problem-solving.

We use mean when the data is normally distributed and median when the data is not normally distributed or there are outliers. However, it’s always a good idea to examine both measures of central tendency and consider the nature of the data before making a final decision.

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