In mathematics, you might have heard about the measures of central tendency. This central tendency is categorized into various types such as mean, median and mode. The mean can be defined as the average score or central value of a given data. The mode can be defined as the number or frequency occurring at the highest time in a particular data whereas the median is regarded as the middlemost value of a given observation. In this article, we will try to cover some basic examples related to the mean, median, and mode formula.
Some Calculations Based on Mean Formula
The mathematical formula given to find the mean of a given data is the sum of all observations divided by a total number of observations. In order to get conceptual clarity about a particular topic, one must solve some examples. Some of the examples are:
Example 1: Find the mean score which is scored by a student if the marks are 45, 65, 80, 48, 50?
Solution:
According to the question,
Marks scored by the student = 45 , 65, 80, 48 and 50.
A total number of observations = 5.
Using the formula of mean, the sum of all observations / by a total number of observations.
45 + 65 + 80 + 48 + 50 / 5 = 57.6
Therefore, the mean or the average score is equivalent to 57.6.
Example 2: Calculate the mean of the given observation: 4, 6, 8, 10, 12?
Solution:
Given that,
Provided Observation = 4, 6, 8, 10, 12.
A total number of observations = 5.
Using the formula of mean, the sum of all observations / by a total number of observations.
4 + 6 + 8 + 10 + 12 / 5 = 8
Thus, the mean is = 8.
Some Calculation Based on Median Formula
The mathematical formula given to calculate the median formula is n + 1 /2th term. Let us try to solve some examples related to the median formula so that this topic becomes clear to you.
Example 1: Calculate the median for the given observation: 3, 4, 8, 6, 9.
Solution:
Given that,
Provided frequency = 3, 4, 8, 6 and 9.
Arranging the frequencies in increasing order = 3, 4, 6, 8 and 9.
Using the formula of median = n + 1 /2th term,
5 + ½ = 3rd term.
Therefore, the median for the given data is equivalent to 6.
Example 2: Find the median for the given observation: 6, 8, 3, 5, 10.
Solution:
Given that,
Provided frequency = 3, 5, 8, 6 and 10.
Arranging the frequencies in increasing order = 3, 5, 6, 8 and 10
Using the formula of median = n + 1 /2th term,
5 + ½ = 3rd term.
Therefore, the median for the given data is equivalent to 6.
Examples Related to Mode
As mentioned above, mode is the highest occurring frequency or observation for a given data. The examples related to mode are mentioned below:
Example 1: What is the mode for the given data: 4, 5, 7, 9, 10, 9.
Solution:
Given that,
Total number of observations = 6.
When arranged in increasing order = 4, 5, 7, 9, 9, and 10.
From the given data it seems that the number ‘9’ occurs the most ( 2 times ).
Therefore, the mode for the given observation is = 9.
Example 2: What is the mode for the given data : 3, 6, 9, 8, 10, and 8?
Solution:
Given that,
Total number of observations = 6.
When arranged in increasing order = 3, 6, 9, 8, 10, and 8.
From the given data it seems that the number ‘8’ occurs the most ( 2 times ).
Therefore, the mode for the given observation is = 8.
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