Measures of Central Tendency
A measure of central tendency is an important aspect of quantitative data. It is a single value that attempts to explain a set of data by identifying the centre point or typical value of a dataset. Its aim is to provide a most accurate description of the entire data. Selecting the best measure of central tendency is depend on the type of dataset you have. The three most common measures of central tendency in statistics are:- Mean
- Median
- Mode
Mean
Arithmetic mean is the most commonly used measure of central tendency . It is calculated as the sum of all the values in the dataset divided by the number of values in the data set. Consider a random variable x and a data set S = {x1, x2, …, xn} of size n which contains possible values of x. So, the mean is {x1, x2, …, xn}/n.
Example: Calculate Arithmetic Mean from the data showing marks of students in a class in a Physics test: 32, 48, 53, 71, 59.
The average mark of students in the Physics test is 52.5.
Median
The median is the middle value of a dataset that has been arranged in the ascending order or in descending order. When the dataset contains an even number of elements, taking the mean of the middle two values.Suppose you have a dataset of five values:
12, 48, 32, 21, 40.
Arrange the values in ascending/descending order, i.e. smallest to largest or largest to smallest.
12, 21, 32, 40, 48.
Here, there are only five values. So, the middle value is 3rd one. That is 32.
Median of the above dataset is 32.Suppose you have a dataset of six values:
12, 48, 32, 21, 40, 36.
Arrange the values in ascending/descending order.
12, 21, 32, 36, 40, 48.
Here, there are six values and the dataset not have a single middle value . So, 3rd and 4th position are the middle of dataset. So, you have to take the 3rd and 4th values in your data set and average them to get a median.
Third and Fourth values are : 32 and 36.
Average of 32 and 36 is : (32+36)/2= 34.
Median of the above dataset is 34.Mode
The mode is the most frequently occurring value in the dataset. If no value repeats, the dataset do not have a mode. It's possible to have no mode , one mode, or more than one mode.Suppose you have a dataset of some values:
12, 48, 32, 21, 32, 36, 54, 21, 78, 32, 18, 94.
Arrange the values in ascending/descending order.
12, 18, 21, 21, 32, 32, 32, 36, 48, 54, 78, 94.
Here the value 32 is occurring three times and the value 21 occurring two times. Mode is the most frequently occurring value in the dataset. 32 is the most frequently occurring value in the dataset.
Mode of the above dataset is 32.
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