We find them in newspapers, articles, in our bank statements, mobile and electricity bills. The list is endless; they are present all around us. Now the question arises if we can figure out some important features of the data by considering only certain representatives of the data. This is possible by using measures of central tendency or averages, namely mean, median, and mode. Let us understand mean, median, and mode in detail in the following sections using solved examples.
Mean, median, and mode are the measures of central tendency, used to study the various characteristics of a given set of data. A measure of central tendency describes a set of data by identifying the central position in the data set as a single value.
We can think of it as a tendency of data to cluster around a middle value. In statistics, the three most common measures of central tendencies are Mean , Median , and Mode. Choosing the best measure of central tendency depends on the type of data we have. The arithmetic mean of a given data is the sum of all observations divided by the number of observations.
For example, a cricketer's scores in five ODI matches are as follows: 12, 34, 45, 50, To find his average score in a match, we calculate the arithmetic mean of data using the mean formula:. Data can be present in raw form or tabular form. Let's find the mean in both cases.
Example: If the heights of 5 people are cm, cm, cm, cm, and cm. Example 2: Here is an example where the data is in the form of class intervals. The following table indicates the data on the number of patients visiting a hospital in a month.
Find the average number of patients visiting the hospital in a day. The value of the middlemost observation , obtained after arranging the data in ascending order, is called the median of the data. For example, consider the data: 4, 4, 6, 3, 2. Let's arrange this data in ascending order: 2, 3, 4, 4, 6.
There are 5 observations. We can see here: 2, 3, 4, 4 , 6 Thus, 4 is the median. To find the median, we need to consider if n is even or odd. If n is odd , then use the formula:. Example 1: Let's consider the data: 56, 67, 54, 34, 78, 43, What is the median?
Arranging in ascending order, we get: 23, 34, 43, 54, 56, 67, Here, n no. Example 2: Let's consider the data: 50, 67, 24, 34, 78, When the data is continuous and in the form of a frequency distribution, the median is found as shown below:. Pre-Algebra Introducing Algebra Overview Operations in the correct order Evaluate expressions Identify properties Equations with variables Coordinate system and ordered pairs Inequalities.
Pre-Algebra Explore and understand integers Overview Absolute value Adding and subtracting integers Multiplying and dividing with integers. Pre-Algebra Inequalities and one-step equations Overview Different ways to solve equations Calculating the area and the perimeter Solving inequalities Understanding inequalities and equations.
Pre-Algebra Discover fractions and factors Overview Monomials and adding or subtracting polynomials Powers and exponents Multiplying polynomials and binomials Factorization and prime numbers Finding the greatest common factor Finding the least common multiple.
Pre-Algebra More about the four rules of arithmetic Overview Integers and rational numbers Learn how to estimate calculations Calculating with decimals and fractions Geometric sequences of numbers Scientific notation. If there are 2 numbers in the middle, the median is the average of those 2 numbers. The mode is the number in a data set that occurs most frequently. Count how many times each number occurs in the data set.
The mode is the number with the highest tally. It's ok if there is more than one mode. And if all numbers occur the same number of times there is no mode. For the data set 1, 1, 2 , 6 , 6, 9 the median is 4. If the size of the data set n is odd the median is the value at position p where. Potential Outliers are values that lie above the Upper Fence or below the Lower Fence of the sample set.
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