Measure of central tendency

The statistic that depicts the center point or value of the dataset measures the central tendency. The three steps of the central tendency are median, mode, and mean. Each of these calculations uses a different method to determine the position of the central point. The data you have will influence which Measure of central tendency you use.

What are the Measures of Central Tendency?

There are three ways to measure central tendency in mathematics: Mean, Mode and Median.

• Mean: The addition of all observations divided by the total number of observations.
• Median: The central value in an organized set.
• Mode: The most frequently occurring value in a data set.

Mean

One of the most fundamental and widely used central tendency metrics is the mean. In mathematics, there are various forms of means. The mean of a set of observations equals the sum of all the values in a collection of data divided by the total number of values in statistics. We may calculate the mean by adding all the values in a data set and dividing it by the total number of values. The overall procedure and formulas, on the other hand, differ depending on whether the data is grouped or ungrouped.

Mean Formula

The mean formula in statistics for a set is the sum divided by the total number of observations. The procedure for calculating the mean will be helpful to solve most of the mean-related problems. Mean = sum of observations/number of observations

Median

For each group, the median is the value in the middle. Half of the data points are more significant, and half of the data points are smaller than the median. The median makes it possible to represent a vast number of data points with just one. It is the most straightforward statistical Measure to compute. The data must be sorted in ascending order to calculate the median, and the middlemost data point is the data’s median.

Median Formula

The median formula can compute the middle value of the arranged group of numbers. It is essential to write the group’s components in ascending order to determine this Measure of central tendency. The median formula changes depending on whether the number of observations is odd or even. The formulas below will assist you in determining the median of the provided data.

Procedure to determine the median

1. Arrange the raw data in an organized form, i.e. ascending or descending
2. Calculate or count the total observation
3. Check whether the number of observations is even or odd.

In case of odd observation Median = (n+1) / 2 where n denotes odd number In case of even observation Median = [(n/2)th term + ((n/2) + 1)th term] / 2

Mode

A value or a number that appears the most frequently in a dataset is called the mode. We may occasionally need to identify a value that occurs more often in the dataset. In such instances, we determine the mode for the given collection of data. A modal value may or may not exist for a particular data set. There may be no mode at all for data with no repeated values. We can also find data with a single mode, three modes, or numerous modes. This is dependent on the dataset.

Mode formula

Determining the mode for ungrouped data is as simple as arranging the data values in ascending or descending order and then looking for repeated values and frequency. The modal value for the supplied data is the observation with the highest frequency, referred to as the modal value. Mode = L + h {(fm−f1) / (f_m−f₁)+(f_m−f₂)} where,

• L is the lower limit of the modal class
• h is the size of the class
• fm is the frequency of modal class
• f1 is the frequency of the class preceding the modal class
• f2 is the frequency of the class succeeding the modal class

Conclusion

The single representative value of a central tendency of a set or the collection of data that recognizes the central is known as the Measure of central tendency. In mathematics, we have three ways to measure the central tendency: mean, mode, and median. Mean is the general way to determine the central tendency of data. The central tendency is one value or single value that describes a set of the database by identifying a central position within a collection of the data. The same concept is also classified as summary statistics. We all have learned about the mean in our previous standard, but we have learned about the other terms like mode and median. These three quantities mode, median, and mean are valid to calculate the central tendency of the raw database.