Median, Mode, and Standard Deviation

Introduction

The central tendency can be defined as a statistical measure that particularly defines the center of a given distribution. There are mainly 3 measures associated with central tendency. These measures are often used in Agriculture engineering and include mode, median as well as mean. Among these means is the one that is often used. On the dispersion or several dispersion measures are real non-negative numbers that help in analyzing the spread of data concerning the central value. These procedures are used for determining whether the whole set of data is squeezed or stretched and are generally of five main types namely variance, range, mean deviation, standard deviation as well as quartile deviations. 

Body 

Median

The Median of the given dataset is represented by its middlemost value. Simply stating, it divides the entire dataset into two halves. The benefit of the calculating median is that it helps in representing several data points with the help of only one data point. It is also very easy to calculate. To compute the median of a given dataset, the entire data needs to be arranged in an order that ascends. In this data which has been arranged in ascending order, the middle point of data gives the median of the overall data. In this context, it should be mentioned that the calculation of the median is dependent on the data point number. If the data points are odd then the median is given by the mid-value within the data. However, if the data points are even then the median is given by the average value of 2 mid values. 

• The formula for median for an odd number of data points is Median = [(n+1)/2]th observation
• The formula for median for even number of data points is 

Median = [(n/2)th observation + (n/2 + 1)th observation]/2

Mode 

The mode can be defined as a measure of central tendency that gives a vague idea regarding the item within a dataset that occurs most frequently. There are several real-life uses as well as the importance of utilizing the central tendency value of mode. While analyzing different types of datasets and handling different questions, instances can occur where the calculation of the central tendency measure of mean might not be enough. For instance, if a college is offering 9 different courses to students and wants to know for which course students are applying the most, then the measures of median or mean will not be suitable. Hence, for these types of cases, the central tendency measure of mode is suitable. 

The mode in the case of ungrouped data can be calculated by arranging the values of data in ascending order or descending order. Next, we need to find the values that are repeating as well as their frequencies. The observation which has the highest frequency is referred to as the modal value of the provided dataset. However, for grouped data, the modal value is given by 

Mode = L + (fm – f1) x h / (fm – f1) + (fm – f2)

where L = lower class limit of modal class, h = class interval, fm = modal class frequency, and f1 and f2 are the frequency of classes preceding and succeeding the modal class.

Standard Deviation

Standard deviation can be described as a measure of dispersion that helps in measuring the degree of scatter or the level of its dispersion concerning the mean. In simple words, it tells us how the provided values are scattered across the sample data. In other words, it is the variability of the data points from the calculated mean. The SD or standard deviation of a statistical population, data set, sample, probability distribution, or random variable is essentially the square root of the variance of the distribution. 

For instance, if we have a total of n observations given by y1, y2, y3, y4, y5,…., yn  then the variance of the given data set is given by 1/n[∑ni=1 (yi – y)2] where y = mean. This measure known as variance can be regarded as an appropriate measure of dispersion and is denoted by σ2. The standard deviation is the root of the previous expression and is denoted by σ.

Conclusion

The overall article has been written on some vital Agricultural Engineering topics. These topics are essentially some measures that are mostly used in statistics to calculate the central tendency or dispersion of a given data series. Median and mode which have been discussed in this article are measures of central tendency, whereas standard deviation is a measure of dispersion.