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Difference between Average and Mean help determine how much data is analysed. Average and mean are the two terms which are often used interchangeably.
- The difference between the Average and Mean can specifically be seen in the topic statistics.
- In statistics, the mean is used in place of the average.
- Average term is defined as a representation of set of numbers by a single value.
- If all the numbers in a set are the same, then their average is also the same.
- Mean is defined as a numeric quantity representing the collection centre of numbers.
- It is used to understand the magnitude and value of a given data set.
- Average and mean are deployed in different situations in our day-to-day lives.
- Creating a budget for the month is a common example of average.
- Insurance agents can use the concept of mean to calculate the mean age of the individuals and offer services accordingly.
- Difference between average and mean can mathematically be represented as:
Average = Sum of Values/Number of Values
Mean = (Sum of all the observations/Total number of observations)
| Table of Content |
Key Terms: Differences between Average and Mean, Average, Mean, Statistics, Arthimetic Mean, Harmonic Mean, Geometric Mean, Numbers, Median, Mode
Average
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Average is defined as the sum of all the given values divided by total number. It is also referred to as arithmetic mean.
- Average is a number which is taken as representative of a list of numbers.
- It is used for those sets which have less difference.
- The average is depicted by the symbol ‘μ’.
- It can be used in the fielf of science and engineering.
- The concept follows the method of monotonicity and linear homogenity.
Average: Sum of given numbers / total numbers
Steps to calculate Average
Following steps must be followed to calculate the average.
- Calculate the sum of all the numbers given in a dataset.
- Next, count the number of samples in a dataset.
- Lastly divide the sum of all numbers with total number of samples.
Example of AverageLet's look at the below examples of an average Example 1: Given values: 3,5,7,8,9,2,4 Sum of above numbers: 3+5+7+9+2+4= 30 Total numbers in the above set: 6 To find out the average: 30/6= 5 Example 2: Given values: 2,4,6,4,4 Sum of the above numbers: 2+4+6+4+4= 20 Total numbers in the above set: 4 To find out the average: 20/4 = 5 |
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| Chapter Related Concept | ||
|---|---|---|
| Empirical Probability | Applications of Integral | Rolle’s Theorem |
Mean
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Mean is the middle point of a set. It is the average value present in the given sets. In other words, it can also be defined as the sum of the smallest & the largest values of the given data divided by 2.
- There are three types of mean such as harmonic mean, geometric mean & arithmetic mean.
- Mean is the summation of a given set of data.
- It is the measure of central tendency.
- The symbol used to represent mean is ‘x̄’.
- Mean can be calculated for grouped and ungrouped data.
Mean = sum of smallest & Largest value in the given data /2
Types of Mean
There are three types of mean are there & they are listed below
Arithmetic Mean
Arithmetic Mean is defined as the total of all the values present in the given set divided by total numbers present in the given sets
Harmonic Mean
Harmonic mean is defined as the reciprocal of arithmetic mean
Geometric Mean
Geometric Mean is defined as that it is almost similar to arithmetic mean but here, we are not adding anything we are multiplying the values and taking the square roots.
Example of MeanLet understand with the example of mean: Example 1: Consider the data set which is given as 3, 5,7,8,9,2,4. Calculate mean? Mean: 2+9/2 11/2= 5.5 Example 2: Consider the data set which is given as 2,4,6,4. Calculate mean? Mean: 2+6/2 8/2= 4 Hence from above data it can be said that average can be a mean but mean can't be an average. |
Difference between Average and Mean
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The difference between average and mean is as follows:
| Average | Mean |
|---|---|
| Average is the sum of all the given values divided by total number is called average | Mean is the sum of the smallest & the largest value of the given data, divided by 2. |
| It is having only one mean that is arithmetic mean | There are three mean namely arithmetic, geometric and harmonic mean. |
| Average is used only when we have sets of values that are more or less the same. | Mean is used when we have a set of values that have more difference |
| It is a single number, which is a representative for all the numbers present in the sets | It is the central point of the set. |
| We can find out the median and mode from the average | We can't find out median and mode from the mean |
| Average is usually used in normal languages such as English and Hindi. | Mean is usually used in technical language that is statistics and maths |
| It is denoted by X bar | It is denoted by µ. |
| This is the formula used for calculating the average: Average: Sum of given numbers / total numbers | This is the formula used for calculating mean: Mean: sum of smallest & Largest value in the given data /2 |
Read More
| Class 11 Maths Related Concepts | ||
|---|---|---|
| Relation and Function | Skewness | Analysis of Variance |
| Relation Between Mean Median and Mode | Mode Formula | Remainder Theorem |
Things to Remember
- The difference between the average and mean can be seen in their formulas.
- Average of any number series is always between the smallest and largest value.
- It will give the approximate value of the data set.
- Mean refers to the middle value of the data set.
- Share price of a company is calculated by using the mean.
Sample Questions
Ques. What is the difference between average & mean? (2 marks)
Ans. Average is the sum of all the given values divided by total number is called average .It is also referred to as arithmetic mean ,whereas the sum of the smallest & the largest value of the given data ,divided by 2 .
Ques. What is the definition of median in statistics? (2 marks)
Ans. Median is defined as the middle value of any given data ,when they are arranged in ascending or descending order .
- Let's have a look on below example
- Given data 24 ,35 ,46, 58,69
- The median for above date is 46
Ques: What is the average of 25 ,50,30,100,200? (2 marks)
Ans: The average of (25+50+30+100+200) /5
= 405/5
= 81
Ques: What is mean of 10,20,30,40,50,60,70,80,90,100? (2 marks)
Ans: To find out the mean of the above data, first we will take the sum of the smallest number & longest number followed by we will divide by 2.
- 10+100/2
- 110/2
- 55
So, the mean for the above set is 55
Ques: Why do we use mean instead of average? (1 mark)
Ans: The reason behind this is that it means to give measurement of central tendency, when we are provided with the grouped data.
Ques: What is the median and mode of 2,2,3,4,5? (2 marks)
Ans: Given data :2,2,3,4.5
- Median: 3
- Mode: mode is nothing but a number which is repeated more than once
- So here, mode would be 2
Ques: Find the average of the following data (46,78,89,10,20)? (2 marks)
Ans: Sum of above numbers: (46+78+89+10+20) = 243
- Total numbers in the above set: 5
- To find out the average: 243/5
- 48.6
Ques: Explain: (A) Is the average value the same as the mean
(B) Name one application of mean? (2 marks)
Ans: (A) Average is nothing but the sum of all numbers divided by total number of values, whereas mean is the mathematical average of two or more data
(B) Mean gives the average of all the data, and all data have equal importance. For example, average salaries of all the working employees in a company.
Ques: A student has gotten the following grades on his tests: 80, 90, 70, and 60. He wants a 75 or better overall. What is the minimum grade he must get on the last test in order to achieve that average? (2 marks)
Ans: Since we don't have a score for the last test, let's use the variable 'a' to determine the average.
- (80 + 90 + 70 + 60 + a)/5 = 75
- We move the five to the other side and multiply 5 with 75.
- 80 + 90 + 70 + 60 + x = 375
- 300 + a = 375
- a = 375 - 300
- x = 75
Ques: Find the mean for the following data: 45, 70, 20, 10, 35? (2 marks)
Ans: Consider the data set: 45, 70, 20, 10, 3
- Mean = Sum of observations/Total number of observations
- = (45 + 70 + 20 + 10 + 35)/ 5
- = 180/5
- = 36
Ques: Find the average value of a given data set: 3, −7, 6, 12, −2? (2 marks)
Ans: First calculate the sum of numbers
- 3 + (-8) + 6 + 12 + (-1)
- 3 – 8 + 6 + 12 – 1
- 12
- Number of units = 5
- Hence, average of data set= 12/5 = 2.4
Ques: Find the mean of the given data set: 10, 6, -3, 2, -7, 10? (2 marks)
Ans: Sum all the numbers first:
- 10+6+(-3)+2+(-7)+11
- 10+6-3+2-7+10 = 28
- Now divide the total from 6, to get the mean.
- Mean = 28/6 = 4.667
Ques: Calculate the average of given terms: 10, 20, 30, 40, 50? (2 marks)
Ans: Sum of all the terms = 10 + 20 + 30 + 40 + 50
- Sum of all the terms = 150
- Total number of terms = 5
- Average = (Sum of all the terms) / ( Total number of terms )
- 150/5
- 30
Ques: Calculate the mean of given terms: 10, 20, 30, 40, 50, 60? (2 marks)
Ans: Smallest number of given terms is 10 and the largest number in the given terms is 60.
- Note here that the terms are in Arithmetic Progression, hence we will use the following formula:
- Mean = (smallest term + greatest term )/2
- ( 10 + 60 ) /2
- 35
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