Statistics Calculators
Mean Calculator

# Mean Calculator

The mean calculator or the average calculator helps you to get the average value of a data set. It divides the data values sum by the data values count to get the average (mean).

Average (x˜) 16.75
Count (n) 16
Sum 268

There was an error with your calculation.

You can use the mean calculator to find a data set's mean or average. It will show the sum of the data values, and the count of the data set values. You can also see the calculation steps.

You just need to type or copy and paste the data. You can copy the data from a spreadsheet or text document. But make sure to separate each number with a comma, space, or new line. The calculator accepts data with mixed delimiters also. Finally, click the "calculate" button.

## The mean

One significant statistic's measure of the central tendency is the mean. The mean is computed by dividing the total of a data set's data values by the count of the data set's values. The mean is used for further statistics calculations because it is based on all values in the data set.

The mean can be computed in a variety of ways, including arithmetic mean, geometric mean, weighted average mean, and so on. In general, the mean in statistics represents the arithmetic mean of a data set.

### The mean of a population

The mean of a population is represented by the Greek letter μ (Mu). Use the below formula to find the mean of a population.

μ = Sum of the data set’s values / Total number of data values in the population

μ = X₁ + X₂ + ⋯ + Xₙ / N

μ = ΣX / N

## The mean of a sample

The mean of a sample is represented by the X̄ (X Bar). Use the below formula to find the mean of a sample.

X̄ = Sum of the data set’s values / Total number of data values in the sample

X̄ = X₁ + X₂ + ⋯ + Xₙ / n

X̄ = ΣX / n

## The Average

In statistics, an average is a single number that can represent an entire set of data values. So any measure of central tendency can be the average. As a result, in statistics, the average is any value that is the data set's mean, median, or mode.

However, in mathematics, the average is determined by dividing the total value of the data set by the total number of items in the data set. When there are two numbers, the sum of the two numbers divided by two is the average between the two numbers. As a result, the average in mathematics has the same meaning as the mean in statistics.

## How to find the average or the mean?

1. Find the total value of the data set.
2. Find the total count of the data set.
3. Divide the total value by the total count of the data set.

The average = The total value of the data set / The total count of the data set

Let’s learn how to find the average of numbers using the below examples.

### Example 1

You've compiled the latest three-match scores of your college cricket team's top six players. Average these numbers and find the best 3 players with the best average scores.

Player Match 1 Match 2 Match 3
Smith 25 30 55
Roy 15 58 20
Jack Not played 25 46
George 30 31 38
Milton 65 17 29
Daniel 55 32 18

Solution

You have to average 3 numbers (Scores). To do that get the total of the 3 numbers and divide it by 3 which is the count.

Smith

Smith's average score = The total Smith's score / Total number of matches = (The 1st match score + The 2nd match score + The 3rd match score) / Total number of matches

Smith's average score = (25 + 30 + 55) / 3 = 110 / 3 = 36.7

Roy

Roy's average score = The total Roy's score / Total number of matches = (The 1st match score + The 2nd match score + The 3rd match score) / Total number of matches

Roy's average score = (15 + 58 + 20) / 3 = 93 / 3 = 31

Jack

Jack has played only 2 matches. Therefore, the average between two numbers of the scores of the 2nd and 3rd match should be taken as Jack’s average score.

Jack's average score = The total Jack's score / Total number of matches = (The 2nd match score + The 3rd match score) / Total number of matches

Jack's average score = (25 + 46) / 2 = 71 / 2 = 35.5

George

George's average score = The total George's score / Total number of matches = (The 1st match score + The 2nd match score + The 3rd match score) / Total number of matches

George's average score = (30 + 31 + 38) / 3 = 99 / 3 = 33

Milton

Milton's average score = The total Milton's score / Total number of matches = (The 1st match score + The 2nd match score + The 3rd match score) / Total number of matches

Milton's average score = (65 + 17 + 29) / 3 = 111 / 3 = 37

Daniel

Daniel's average score = The total Daniel's score / Total number of matches = (The 1st match score + The 2nd match score + The 3rd match score) / Total number of matches

Daniel's average score = (55 + 32 + 18) / 3 = 105 / 3 = 35

So, you can create a summary table like this.

Player Average Score Rank
Smith 36.7 2
Roy 31 6
Jack 35.5 3
George 33 5
Milton 37 1
Daniel 35 4

The top 3 players are Milton, Smith, and Jack, according to the above table.

Using the mean/average calculator, you can easily get the average score for each player by simply copying each line in the table. Following that, you can quickly create the final average score summary table.

### Example 2

The data set below shows the average semester scores for students enrolled in the MBA Finance (Special) program. A special award will be given to the student with the highest overall average score at convocation. Who will win this award?

Student Semester 1 Semester 2 Semester 3 Semester 4 Average
Susan 66 71 60 47 (66 + 71 + 60 + 47) / 4
Richard 58 73 50 47 (58 + 73 + 50 + 47) / 4
Thomas Exempt 82 47 82 (82 + 47 + 82) / 3
Charles 67 47 66 66 (67 + 47 + 66 + 66) / 4
Jessica 47 83 52 61 (47 + 83 + 52 + 61) / 4
Karen 63 56 65 62 (63 + 56 + 65 + 62) / 4
Lisa 64 63 62 85 (64 + 63 + 62 + 85) / 4
Ronald 68 66 69 81 (68 + 66 + 69 + 81) / 4
Jacob Exempt 64 66 77 (64 + 66 + 77) / 3
Rebecca 70 84 62 51 (70 + 84 + 62 + 51) / 4

Now you can create a summary table like below.

Student Overall average score Rank
Susan 61.00 8
Richard 57.00 10
Thomas 70.33 2
Charles 61.50 6
Jessica 60.75 9
Karen 61.50 6
Lisa 68.50 4
Ronald 71.00 1
Jacob 69.00 3
Rebecca 66.75 5

As per the above table, Ronald has the overall highest average score. Therefore, Ronald will win the special award at the convocation.

For the example above, you can use the mean calculator. The overall average score for each student can be easily found by merely copying each line of the table. As a result, you do not need to calculate the total score and the total number of semesters separately for each student. You will quickly get the average score for each student, and you can quickly build the overall average score summary table.

## The Use of the Knowledge About Average and Mean in Real Life

### Healthcare

• Pediatricians compute the typical weight of newborns to find trends.
• Medical representatives examine the average prices of all generic pharmaceutical brands before setting prices for new products.

### Real Estate

• Real estate brokers compute the average price of lands and homes to inform their clients about the current price ranges.
• For forecasting purposes, real estate companies compute typical broker fees.

### Human Resources

• Human resource departments typically calculate the average pay for new hires in the market. It is helpful to budget for new talent acquisitions.
• The HR departments must budget an average amount for employee welfare initiatives. They could find it easier to keep their spending on employee welfare within the spending limit.

### Marketing

• Marketers typically calculate average sales per customer to monitor the growth of average sales per customer.
• They calculate average sales per advertisement to ensure their marketing spending is used effectively.

### Education

• The average number of students per teacher is calculated by educational institutions to establish a productive learning environment.
• The average student grade is frequently calculated by educational institutions to understand the overall progress of their institution.

### Sports

• To determine whether a bowler is a fast bowler in cricket, the average balling speed is calculated.
• To determine performance patterns, average running scores for batsmen are computed in cricket.