Data is present everywhere, and we encounter them daily. So it becomes necessary to be able to work out the important features of a given dataset considering only some definite representatives of the data. Here the measures of central tendency come in handy. Central tendency is a statistical measure that aims at providing an accurate description of an entire data set. It classifies a single value as the representative of the collected data. The three most commonly used central tendency measures are mean, median, and mode.
Mean, median, and mode do not give information concerning only individual data from the given dataset but summarize an entire dataset and provide a single value to represent the data. Let us discuss the three measures and understand how they can perform depending on the properties of the data.
Mean
Mean is used to provide an average value of a given dataset. The mean is calculated by adding all the values of the given dataset and then dividing it by the number of values present. This form of mean is generally the arithmetic mean. There are also other mean measures such as geometric, harmonic, and weighted. When the values provided in a data set are the same, the means of geometric, weighted, hegemonic, and arithmetic measures will be the same. But with variability in the data, the values of the mean will also differ.
Mean is represented by the lowercase Greek letter “mu” which is denoted as μ. Mean is used to calculate both continuous and discrete data. An important feature of the mean is that all the values present in a given data set are a part of the mean calculation.
Median
Median is used to calculate the middle-most value in a given dataset. The median is calculated after the values are set in an ascending or descending order. Calculating the median is simple when there is an odd number of values, for instance, if we have a data set of 11 numbers, after arranging them in an ascending or descending order, we can identify the median that is the value that lies in the middle. But when we have an even number of values in a dataset, the median is calculated by taking the two middle-most values and finding their mean. The answer to that is called the median of that particular data set.
Mode
Mode is a measure that identifies the most frequently occurring value in a given dataset. Sometimes there may be multiple modes. It happens when a few terms present in a dataset occur with equal frequency, while sometimes there might be no modes at all. When there are two modes present in a distribution, it is called bimodal. And when there are three modes present in a distribution, it is called trimodal. Mode is commonly used when there is categorical data. We use it to find the most common category.
Selection of central tendency measure based on the properties of the data:
When a dataset consists ofa symmetrical distribution of continuous data, all three measures are helpful. When it has a skewed distribution, the median is more helpful. For categorical data, the mode is the best measure. And for original data, median and mode both work equally well.
So, we learned that central tendency is a statistical measure that is the value used to represent or summarize a distributed data set. We also learned that there are three commonly used measures of central tendency, namely mean, median, and mode. And all these measures work for a different set of data depending on the data properties.
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