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Home > News & Articles > Mean Statistics Formula: Definition, Mean for Grouped and Ungrouped data, Calculation, and Types
Updated on 08th February, 2023 , 7 min read
Mean statistics formulas are fundamental to the study of mathematics and data science. They can tell us a lot about how certain variables interact with each other, and they are essential to understanding both basic and complex relationships between numbers or patterns. In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given collection. It indicates that values in a certain data collection are distributed equally. The three most often employed measures of central tendency are the mean, median, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to get the mean. When all of the values are organized in ascending order, the median is the median value of the provided data. While the number on the list that is repeated the most times is known as the mode.
The mean is the average of the given numbers and is computed by dividing the total number of numbers by the sum of the given numbers.
Mean is equal to (Sum of All Observations/Total Observations).
Usually, the letter "x" is used to represent the mean. The bar above the letter x represents the average of X values.
Mean statistics is the study of the mathematical properties of numerical data sets. It is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. In applying statistical methods to a data set, one can often make inferences about the population that the data set represents.
In order to calculate mean statistics, you will need to first determine the sum of all the data points. Once you have determined the sum, you will then divide this by the total number of data points. This will give you the mean statistic.
The basic formula for calculating the mean is determined by the data collection. When calculating the mean, every term in the data set is taken into account. The standard mean formula is the total number of phrases divided by the sum of all terms. For example, if you roll the dice ten times and get an average roll of 4, your mean score would be 4. If you rolled three times and received a 3, 9, and 12, your mean would be 6 (12  3).
The mean is equal to the product of the given data and the total amount of data. We must first add up (sum) all of the data values (x) in order to get the arithmetic mean of a set of data, and then divide the result by the total number of values (n). Since the symbol for summarizing values is (see Sigma Notation), we arrive at the formula shown below for the mean (x):
xÌ„=∑ x/n
The mean is the sum of all the values divided by the number of values. It's also called the average or expected value.
For example, if you roll the dice ten times and get an average roll of 4, your mean score would be 4. If you rolled three times and received a 3, 9, and 12, your mean would be 6 (12  3).
In statistics, the mean is the sum of all the values in a data set, divided by the number of values in the data set. The mean can be calculated for numerical data sets and for categorical data sets.
To calculate the mean for a numerical data set, add up all the values in the data set and divide by the number of values in the data set. For example, if you have a data set with five values: 1, 2, 3, 4, and 5, the mean would be (1+2+3+4+5)/5 = 15/5 = 3.
To calculate the mean for a categorical data set, count how many times each category occurs and divide by the total number of values in the data set. For example, if you have a data set with two categories: Category A occurs three times, and Category B occurs seven times, then (3+7)/2 = 10/2 = 5.
The example given below will help you understand how to find the mean of ungrouped data.
Example:
In a class, there are 20 students, and they have secured a percentage of 88, 82, 88, 85, 84, 80, 81, 82, 83, 85, 84, 74, 75, 76, 89, 90, 89, 80, 82, and 83.
Find the mean percentage obtained by the class.
Solution:
Mean = Total of percentage obtained by 20 students in class/Total number of students
= [88 + 82 + 88 + 85 + 84 + 80 + 81 + 82 + 83 + 85 + 84 + 74 + 75 + 76 + 89 + 90 + 89 + 80 + 82 + 83]/20
= 1660/20
= 83
Hence, the mean percentage of each student in the class is 83%.
For grouped data, we can find the mean using either of the following formulas.
Direct method:
Mean,xâ€•=∑i=1nfixi∑i=1nfi
Assumed mean method:
Mean,(xâ€•)=a+∑fidi∑fi
Stepdeviation method:
Mean,(xâ€•)=a+h∑fiui∑fi
Go through the example given below to understand how to calculate the mean for grouped data.
Example:
Find the mean for the following distribution.
xi 
11 
14 
17 
20 
fi 
3 
6 
8 
7 
Solution:
For the given data, we can find the mean using the direct method.
xi 
fi 
fixi 
11 
3 
33 
14 
6 
84 
17 
8 
136 
20 
7 
140 
∑fi = 24 
∑fi xi = 393 
Mean = ∑fixi/∑fi = 393/24 = 16.4
We have seen examples of finding the mean of positive numbers until now. But what if the numbers on the observation list include negative numbers. Let us understand with an example:
Find the mean of 9, 6, 3, 2, 7, and 1.9+6+(3)9+6+(3) +2+(7)+1 = 9+63+27+1 = 8
Now divide the total by 6, to get the mean.
Mean = 8/6 = 1.33
The main types of mean, including:
The average of a set of data can be calculated by adding up all the values in the data and dividing by the total number of values. For example, to find the average price of 10 clothing materials, the sum of all the prices is divided by 10. To find the average age of students in a class, the sum of the ages of all the students is divided by the total number of students in the class.
Q.1: Calculate the mean of the numbers 5, 10, 15, 20, 25.
Q.2: Determine the mean of the data set: 10, 20, 30, 40, 50, 60, 70, 80, 90.
Q.3: Determine the mean of the first 10 even numbers.
Q.4: Determine the mean of the first 10 odd numbers.

Statistics formulas are essential tools for understanding data and making sense of it. A thorough understanding of mean statistical formulas is required to get the most out of statistical analysis. Thankfully, there are many resources available to help you gain an indepth understanding of these formulas so that you can confidently use them when working with data sets. Whether you're interested in pursuing a career as a statistician or simply want to improve your skill set, learning more about statistical concepts such as the mean statistics formula is definitely worth your time.
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By  Nikita Parmar 20240524 16:30:15 , 4 min readThe ratio between the sum of all observations and the total number of observations in a data collection is known as the mean in statistics. As an example, the mean of 2, 6, 4, 5, 8 is Mean = (2 + 6 + 4 + 5 + 8) / 5 = 25/5 = 5.
The types of mean are Arithmetic Mean, Geometric Mean, Weighted Mean and Harmonic mean.
The first 10 natural numbers are: 1,2,3,4,5,6,7,8,9,10 Sum of first 10 natural numbers = 1+2+3+4+5+6+7+8+9+10 = 55 Mean = 55/10 = 5.5
The relationship between mean, median, and mode is given by: 3 Median = Mode + 2 Mean.
The first 5 composite numbers are 4, 6, 8, 9 and 10. Thus, Mean = (4 + 6 + 8 + 9 + 10)/5 Mean = 37/5 = 7.4 Hence, the mean of the first 5 composite numbers is 7.4.
The average is obtained by dividing the total of all values in a data set by the number of values. This calculation can be performed on raw data or data that has been aggregated in a frequency table.
The mean or average of a data set can be calculated through these two steps: 1) sum up all the values, and 2) divide the sum by the number of values.