# Mean in Math: Meaning, Statistics along with Types & Formulas (2023)

Mean Definition: A mean in simple words can be understood as the mathematical average of a set of two or more numbers. The mean for a provided set of numbers can be estimated in more than one way, comprising the arithmetic mean method, which is practiced to compute the sum of the numbers in the series, and the geometric mean approach, which is the average of a set of products. Though, all of the primary means of computing a simple average produce the same estimated result is obtained most of the time.

With this article on mean, you will be able to answer questions like what is meant by mean? or what is the meaning of mean? define mean in math, statistics and every information related to meaning. So go through the entire article and develop your knowledge regarding Mean.

Learn about Mean Median Mode

## What is the Meaning of Mean in Maths?

Mean, in Maths, is the final average value of the provided numbers or data. To determine the mean, we first require to add the total values provided in a datasheet and then divide the total sum by the total number of values/number given. Assume, in a given data table, the price values of 14 chairs are mentioned. If we have to determine the mean of the prices, then add the prices of each chair and divide the total sum by 14. It will appear in an average value.

Mean = (Sum of all the observations/Total number of observations)

Example: What is the mean of 2, 4, 8, 6 and 12?

Step 1: First add all the numbers.

2+4+6+8+12 = 32

Step 2: Now divide by 5 (here 5 is the total number of observations).

Mean = 32/5 = 6.4

Consider another example, where we have to determine the average age of teachers in a school. Here also we will apply the same procedure. First, add the individual age of all the teachers and then divide the sum by the total number of teachers present in the school.

## Mean Meaning in Statistics

Mean is an approach that is generally used in Statistics. At our school level, we learned the theory behind the average calculation. However, in higher levels, we are introduced to the topic called mean.

Mean is a fundamental concept in mathematics and statistics. In statistics, it is defined as the measure of the central tendency of a probability distribution with median and mode. It is also recognized as the expected value.

(Video) Math Antics - Mean, Median and Mode

Mean is nothing but the advanced version of average for a sequence or series of a number. In the actual world, when there is enormous data prepared, we practice statistics to deal with the calculations. Along with mean, statistics also include important terms like median and mode.

The Median is defined as the middle value of a given data/information/number when all the values are arranged in ascending order. The Mode is the number in the list, which appears for the maximum number of times. Mean is a statistical concept that carries major importance in finance. The concept is applied in various financial fields, including management and business valuation.

Check Rolle’s Theorem and Lagrange’s Mean Value Theorem

## Types of Mean

There are majorly 3 distinct types of mean value that you will find in statistics.

• Arithmetic Mean
• Geometric Mean
• Harmonic Mean

### Arithmetic Mean

The Arithmetic Mean is the average of the numbers/data or can be understood as the calculated central value of a set of numbers. To determine Arithmetic Mean:

• Add all the numbers/data given.
• Divide the total obtained in the above steps by the total numbers/data.

$$X=\frac{\sum_{i=1}^nX_i}{N}$$

Here N= Total number of observations.

Learn about Assumed Mean Method

### Geometric Mean

The Geometric Mean or GM is the average value or mean which implies the central tendency of the set of numbers by using the root of the product of the values. Below is the formula for the Geometric Mean calculation.

$$Consider,\ if\ x_1,x_2\dots.\ x_n\ are\ the\ observation,\ then\ the\ G.M\ is\ defined\ as$$

$$GM=\sqrt[n] {x_1\times x_2\times x_3…..x_n}$$

$$GM=(x_1\times x_2\times x_3…..x_n)^{\frac{1}{n}}$$

This can also be written as;

(Video) Mean, Median, and Mode of Grouped Data & Frequency Distribution Tables Statistics

$$\log G.M=\frac{\sum_{ }^{ }\log\ x_i}{n}$$

$$GM=Anti\log\ \frac{\sum_{ }^{ }\log\ x_i}{n}$$

$$G.M.=\sqrt[n]{\prod_{i=1}^nx_i}$$

$$For\ any\ Grouped\ Data,\ G.M\ can\ be\ written\ as:GM=Anti\log\ \frac{\sum_{ }^{ }f.\log\ x_i}{n}$$

Thus, the geometric mean is also represented as the nth root of the product of n numbers. values.

### Harmonic Mean

Harmonic Mean or HM is determined as the reciprocal of the average of the reciprocals of the data values. The harmonic mean formula is applied to calculate the average of a set of numbers.

$$Ifx_1,\ x_2\ ,\ x_3,\dots,\ x_{n\ }are\ the\ individual\ items\ then;$$

$$H.M=\frac{n}{\frac{1}{x_1}+\frac{1}{x_2}+\frac{1}{x_3}+\dots+\frac{1}{x_n}}=\frac{n}{\sum_{i=1}^n\frac{1}{x_i}}$$

$$For\ a\ frequency\ distribution,\ the\ harmonic\ mean\ formula\ is:$$

$$H.M=\frac{N}{\sum_{i=1}^nf\frac{1}{x_i}}$$

Here N=summation of f.

In general, the harmonic mean is used when there is a requirement to give higher weight to the smaller items. It is used in the case of times and average rates.

### Important Points on Mean

• The mean is the arithmetical average of a set of two or more numbers.
• Arithmetic mean geometric mean and harmonic mean are three types of mean that can be calculated.
• Summing the numbers/data in a set and dividing it by the total number provides the arithmetic mean.
• The geometric mean is somewhat complicated and includes the multiplication of the numbers using the nth root.
• The mean serves to evaluate the performance of an investment or company over a while, and several other uses.
• Average is different from an Arithmetic Mean.

We hope that the above article on Mean is helpful for your understanding and exam preparations. Stay tuned to the Testbook app for more updates on related topics from Mathematics, and various such subjects. Also, reach out to the test series available to examine your knowledge regarding several exams

(Video) What are Mean, Median and Mode? | Statistics | Don't Memorise

 If you are checking Mean article, also check the related maths articles in the table below: Area of a Triangle Area of a Circle Circumference of a Circle Parabola Mean Deviation Lines of Regression

## Mean FAQs

Q.1How do you define the mean?

Ans.1 The mean in mathematics is defined as the average of a set of two or more numbers. Summing the numbers in a set and dividing by the total number provides the arithmetic mean.

Q.2What is the “mean” in maths?

Ans.2 The mean is the sum of the numbers divided by the total numbers present. To find the mean, add all the numbers commonly then divide by the number of numbers. Eg 3 + 6 + 100 + 13 + 3 = 125 ÷ 5 = 25. The mean of the range of numbers is 25.

Q.3What is “mean” in statistics?

Ans.3 The mean or the average of a data set is determined by adding all numbers in the data set and then dividing by the number of values available in the set.

Q.4What is the difference between mean and average?

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Ans.4 The term Average is the sum of all the data divided by the total number of values in the set. Whereas in Mean we find the average of a sample data. In other words average is finding the central value in mathematics, whereas mean is finding the central value in statistics.

Q.5What is “mean” and its uses?

Ans.5 The mean is the sum of the numbers in a data set divided by the total number of values in the set. The mean is also understood as the average. Mean is suitably used for a data set with numbers that are nearby together.

Q.6What is “mean” and its types?

Ans.6 Mean is the most generally adopted model of central tendency. There are different types of the mean; arithmetic means, geometric mean (GM) and harmonic mean (HM).

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