and Median of a Set of Data

When you analyze any given data set, there are several different descriptive statistics that you can calculate to gain a better understanding of its distribution and overall shape. Two of the most commonly used measures of central tendency, which provide insight into the central or typical values in a set of data, are the mean and the median.

If you are unfamiliar with these terms or are unsure about how to find them, then you will benefit from reading this guide. In this article, we will walk you through the steps of finding the mean and median of a set of data and explain when each measure is most appropriate to use.

What is the Mean?

The mean, also known as the arithmetic mean or average, is a measure of central tendency that represents the typical value in a set of data. To find the mean, you need to add up all the values in the data set and divide the sum by the total number of observations. To make it simpler, just follow these steps:

1. Add up all the values in the data set

2. Divide the sum by the total number of observations

For example, consider the following data set: {2, 3, 5, 7, 9}

To find the mean, you add up all the values and divide by the total number of observations:

Mean = (2 + 3 + 5 + 7 + 9) / 5

Mean = 26 / 5

Mean = 5.2

Therefore, the mean of this data set is 5.2.

It is important to note that the mean is sensitive to the influence of outliers, which are extreme values that may be vastly different from the rest of the data set. An outlier can skew the mean and create a misleading representation of the typical value in the data. For this reason, the mean is best used when the data are normally distributed or when there are no extreme values that could significantly impact its calculation.

What is the Median?

The median is another measure of central tendency that represents the middle value of a set of data. To find the median, you must first arrange the data in numerical order and then determine the value in the middle of the data set.

If the data set contains an odd number of observations, then the median is the middle value. If the data set contains an even number of observations, then the median is the average of the two middle values.

To make it simpler, follow these steps:

1. Put the data in order from least to greatest

2. If the number of observations is odd, the median is the middle value in the data set

3. If the number of observations is even, the median is the average of the two middle values

For example, consider the following data set: { 4, 5, 7, 8, 10, 12, 13}

To find the median, you must first arrange the data in ascending order:

{ 4, 5, 7, 8, 10, 12, 13}

Since there are 7 observations, an odd number, the median is the fourth value:

Median = 8

Therefore, the median of this data set is 8.

The median is not sensitive to outliers, or extreme values, and is better used when the distribution of the data is skewed, or when there are significant outliers present in the data set. The median is also often used as a measure of central tendency when the data set contains values that are not numeric. This is because the median can be calculated without relying on numerical values and can be used to compare sets of data with different units of measurement.

Conclusion

Both the mean and median are useful tools in descriptive statistics that enable us to gain insight into the central tendencies of a data set. The mean is sensitive to outliers and is best used when the data are normally distributed. The median, on the other hand, is not sensitive to outliers and is better used when the data are skewed or contain significant outliers.

By following the steps outlined in this article, you can easily calculate both the mean and the median of any given data set. It is important to remember to use the appropriate measure of central tendency depending on the characteristics of the data set you are analyzing. With these concepts and tools in mind, the next time you encounter a data set, you will be well-equipped to analyze and interpret its results.