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Do You Know Mean Formula?
There are various instances in our day-to-day life where we need to find the average value for a given data. In order to find the average or mean value of a given data, the mean formula is used. The mathematical formula for the mean is classified into two types: for grouped data and for ungrouped data.
The formula for grouped data: Sum of total frequencies / total number of observations. We may solve some examples based on the grouped data of mean and understand the concept.
Some Examples Based on the Mean Formula
As it is mentioned in the first paragraph, the mathematical formula to calculate or find the mean of a given data or observations is the Sum of total frequencies / total number of observations. Let us solve some examples so that this topic becomes clearer to you. Some of the examples are mentioned below:
Example 1: Calculate the mean or average marks scored by a student in the examination if the observations are as follows: 45, 86, 98, 100, 69?
Solution: Given that,
Frequencies / Marks = 45, 86, 98, 100, 69.
When arranged in ascending order = 45, 69, 86, 98 and 100.
A total number of observations = 5.
Using the formula to find the average marks = Sum of total frequencies / total number of observations.
45 + 69 + 98 + 86 + 100 / 5 = 398 / 5
398 / 5 = 79.6 .
Therefore, the average mark scored by the student is equivalent to 79.6 .
Example 2: Find the mean of the first five natural numbers using the mean formula?
Solution: According to the question,
First five natural numbers = 1, 2, 3, 4, and 5 (we do not consider 0 as a natural or counting number).
Thus, frequencies = 1, 2, 3, 4, 5 (arranged in increasing or ascending order).
Total number of Frequencies = 5.
Using the formula to find the mean of the first five natural numbers = Sum of total frequencies / total number of observations.
1 + 2 + 3 + 4 + 5 / 5 = 15 / 5
15 / 5 = 3
Therefore, the mean of the first five natural numbers is equivalent to 3.
What is Mode?
There are various types of central tendency in statistics, one of them is the mode. It can be defined as the value or frequency that occurs at the highest time in a given observation. A mode is classified into various types such as bimodal, trimodal, multimodal, unimodal. The unimodal list signifies that the given data consists of only one mode. Similarly, bimodal and trimodal signifies a data has 2 and 3 modes respectively. We shall solve some examples of unimodal lists in the next few coming sections.
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Some of the Examples Based on Mode
We already know that there is no such specific formula to find the mode of a given data if the list is unimodal. The mode of the given observation will be equivalent to the highest number of occurrences of the frequency. Some of them are listed below:
Example 1: Find the mode of the given data if the observations are as follows: 2, 6, 8, 3, 5 and 2 ?.
Solution: Given that,
Frequency = 2, 6, 8, 3, 5 and 2.
When arranged in increasing order = 2, 2, 3, 5, 6, and 8.
From the above data, it is clear that the number ‘2’ has the most occurrence. Thus, the mode of the given data is equivalent to 2.
Example 2: Find the mode of the given data if the observations are as follows: 2, 6, 8, 3, 5 and 3 ?.
Solution: Given that,
Frequency = 2, 6, 8, 3, 5 and 3.
When arranged in increasing order = 2, 3, 3, 5, 6, and 8.
From the above data, it is clear that the number ‘3’ has the most occurrence. Thus, the mode of the given data is equivalent to 3.
In order to study about mode and mean formulae in a detailed and interesting manner, visit Cuemath and book a free session now.