What is Mean & its Importance: A Complete Guide for Students
Read Time: 5 mins
Understanding of statistical concepts is important for every student to succeed in academic life. It has many essential concepts, such as median, mode, critical value, standard deviation, and more. These concepts are all used in different fields, from student life to professional life.
Mean is also one of the basic and useful concepts of statistics. It helps to understand data better and compare different sets of numbers easily. You can get help with this by checking test scores, analyzing survey results, or measuring the temperature.
This means it provides a quick overview of what the data looks like overall. This guide will explain the definition of mean, how to calculate it, the different types of means, and why it’s so important for students.
What is Mean in statistics?
Mean is one of the statistical concepts used to measure the central tendency of a dataset. It is calculated by adding all the numbers together and dividing the total by the number of values present. The mean provides one value that is useful for summarizing the whole dataset. This makes it easier to understand and compare different sets of data.
Symbol of Mean: It is mostly represented by the “x̄”. The bar that is above the x represents the mean of x number of values.
Formula of Mean
The formula of the mean depends on the type of data. If the data is in ungrouped form, then we can use the following formula,
Ungrouped Mean Formula:
x̄=∑ x/n
Grouped Mean formula: If the data is in grouped form, then use the formulas below to calculate the mean. The coming section will clarify the use of these formulas with examples.
Breakdown of the terms used in formulas:
fi = frequency of the ith class
xi = Midpoint of the ith class
a: Assumed mean
di = xi – a
ui = xi – a / h
h: Class width
Importance of Mean
The mean, which is often referred to as average, is of great importance in statistical analysis for several reasons. Some of them are given below:
- It provides a measure of central tendency and summarizes data by a single value. Additionally, helps to understand where most of the data lies.
- Mean helps researchers by reducing the large data into a single value. This makes it easy for them to interpret and communicate findings.
- The average is also used to calculate different statistical concepts, such as standard deviation, variance, and covariance.
- You can compare different groups using their means. For example, comparing average marks between two classes.
- The mean helps students understand math problems better. It also helps in subjects like science, economics, and statistics.
How to Calculate the Mean?
To find the mean manually, you need to check the nature of the data. If it is grouped, then you can apply the direct, substitution, or squared method. If it is ungrouped, then use the general formula of the mean. Let’s go through both types of examples to understand. But if you want to do it quickly with 100% accuracy, then use a mean calculator.
For manual method understanding, see the examples below.
Example of ungrouped data:
A teacher wants to calculate the average score of 5 students on a math quiz. The marks (out of 10) obtained by the students are: 8, 6, 9, 7, 10.
Solution:
Use the formula:
Mean = Sum of obtained marks / Number of students
Sum of obtained marks = 40
Number of students = 8
Put in the formula:
Mean = 40 / 5 = 8
The average score of the students is 8 marks.
Example for Grouped Data
Suppose the following data set, which represents the scores obtained by students on a paper. The marks in grouped into intervals:
Calculate the mean of the given data.
Solution
Follow the steps below to calculate the mean of grouped data.
Step 1: Calculate the Midpoints
Step 2: Calculate the Sum of (f *x).
Σ(f⋅x) =5+22.5+87.5+157.5+22.5=295
Step 3: Calculate the Total Frequency.
Σf = 2+3+7+9+1=22
Step 4: Calculate the Mean.
Mean = Σ(f⋅x)/ Σf
=295/ 22
≈13.40
The mean of the grouped data is approximately 13.40.
Final Thoughts
The mean is an important statistical measure that simplifies data by providing a central value. It’s calculated differently for grouped and ungrouped data. But its purpose remains the same: to offer a clear summary. For students, an understanding of the mean is essential for academic success in various subjects. It enables them to analyze information, compare datasets, and draw meaningful conclusions.
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