In math, a mean represents the average of a set of numbers and is referred to as a central value. In other words, the mean formula is the average of the values in the set. Aside from the mode and median, the mean is one of the measures of central tendency in statistics. However, all three measures (mean, median, and mode) together define the central value of a set of data or observations.
Formula of Mean = (Sum of all the observations/Total number of observations)
The basic formula for calculating the mean is based on the data set provided. Each term in the given dataset is considered when calculating the mean. The general formula for mean is the ratio of the sum of all terms to the total number of terms. As a result, we can say;
Mean = Sum of the Data Given/Total Number of Data
To find the arithmetic mean of a set of data, add up (sum) all of the given data (x) and afterward divide the value by the number of values (n). Because is the symbol used to indicate that values should be summed (see Sigma Notation), we get the following formula for the mean (x):
Definition of Mean and Mode in Statistics
The mean is simply the average of the given set of values. It refers to the distribution of values in a given data set that is equal. The statistical measure of central tendency recognizes a single value as representative of the entire distribution. It makes every effort to provide an accurate description of the entire data set. It is the one-of-a-kind value that represents the collected data. The three most commonly used measures of central tendency are the mean, median, as well as mode. Mode is that value in the data which comes more frequently.
The mean of a discrete probability distribution of a random variable X equals the sum of all possible values weighted by the probability of that value; that is, it is computed by adding the products of each possible value x of X and its probability P(x).
Want to understand the basic concept of mean as well as median, you can visit the Cuemath website.
Mean of Negative Numbers
So far, we’ve seen examples of finding the mean of positive numbers. But what if the observation list contains negative numbers? Let us illustrate with an example:
Example: Find the mean of the given numbers 9, 6, -3, 2, -7, 1.
Add all the numbers first:
Total: 9+6+(-3)+2+(-7)+1 = 9+6-3+2-7+1 = 8
Divide the total by 6 to obtain the mean.
Mean = 8/6 = 1.33
Mean Symbol (X Bar)
The symbol for the mean of various observations is usually represented by the letter ‘x.’ The bar above the letter x represents the average of x values.
X̄ equals (Sum of values ÷ Number of values)
Types of Mean
In statistics, you will primarily be studying three different types of mean value.
- Arithmetic Mean
- Geometric Mean
- Harmonic Mean
Arithmetic Mean is defined as the sum among all values divided by the number of values. To calculate, add all of the given numbers together and divide by the number of numbers given.
Example: Find the mean of 3, 5, 9, 5, 7, 2?
Now add up all the given numbers:
3 + 5 + 9 + 5 + 7 + 2 = 31
Now divide by how many numbers are provided in the sequence, that is the number of observations:
5.16 is the answer.
xy is the geometric mean of two numbers, x and y. The geometric mean of three numbers, x, y, and z, is 3xyz.
Geometric Mean =
To average ratios, the harmonic mean is used. The harmonic mean(H.M.) of two given numbers x & y is 2xy (x+y). The harmonic mean of three numbers x, y, and z is 3xyz(xy+xz+yz).
Harmonic Mean = n/(1/x_1 + 1/x_2 + 1/x_3 +……+ 1/x_n )