Mean in Math: Definition, Examples, and Applications
By Indeed Editorial Team
Published June 4, 2022
The Indeed Editorial Team comprises a diverse and talented team of writers, researchers and subject matter experts equipped with Indeed's data and insights to deliver useful tips to help guide your career journey.
When analyzing data at work, whether financial, numerical, or statistical data, you may need to calculate the mean of the data to complete your analysis. You might require the mean of your data set if you are an accountant, human resources professional, data or business analyst, computer programmer, statistician, teacher, mathematician, or operations researcher. Understanding what a mean is in math and its real-life applications in a work environment can help you with your day-to-day operations. In this article, we explore mean in math, examples of how you calculate the mean, and its useful applications in a work environment.
What is the mean in math?
There are several professional instances in which you may benefit from understanding the definition of mean in math. The mean, also called the average, is a mathematical calculation that finds the central or typical value in a set of data. It is the middle value of a set of numbers and you calculate the mean by dividing the sum of a group of numbers by the total amount of numbers in the dataset. To find the mean, you first add up all the individual values in the dataset. After you have the total value of all numbers in the dataset, you count how many values are in the list and divide the sum by that number. Below is the calculation for finding the mean:
Mean = sum of the values in a given data/total number of values
Examples of calculating the mean
Knowing how to calculate the mean is useful in many scenarios at work when making strategic decisions, allocating resources, or planning for the future. Here are some example scenarios where it's beneficial to find the mean in a dataset:
1. Finding average spending for budgets
It's nearing the end of the fiscal year. Your manager asks you to determine how much each department has spent over the last year. This is to help plan the next year's budget accordingly.
Finding the mean can help you identify how much money each department spends each year and whether departments are usually over or under budget. Your manager can use this information to determine the budget allocation for each department and whether they need to ask certain departments to be more conscious of their spending. As you review the financial information for the human resources department, you record the following spending over the last 12 months:
You add up these numbers and get a total of $55,193 spent throughout the entire year. When you divide this number by 12, you get average spending of $4,599.42 per month for the human resources department. Now, you can compare this number against averages from previous years and their allocated budget for the current year to determine their budget for the coming year.
2. Evaluating sales from different branches
A store owner has retail locations in three different cities and they want to know how much each store sells each week. They want this information to determine how well each store is performing in terms of sales and customer satisfaction to help them plan inventory and staff training sessions. According to transaction records, the store owner obtains the following information about weekly sales for each of their locations:
The first store sells the following quantities:
Monday: 40 units
Tuesday: 35 units
Wednesday: 100 units
Thursday: 87 units
Friday: 140 units
Saturday: 200 units
Sunday: 180 units
They add up the total number of units and divide by seven, which gives an average of 111.71 units sold throughout the week.
The second store sells the following quantities:
Monday: 60 units
Tuesday: 96 units
Wednesday: 132 units
Thursday: 70 units
Friday: 110 units
Saturday: 125 units
Sunday: 130 units
They find the total number of units sold throughout the week, which is 723 units, and divide by seven to get an average of 103.29 units sold.
The third store sells the following quantities:
Monday: 76 units
Tuesday: 80 units
Wednesday: 60 units
Thursday: 102 units
Friday: 145 units
Saturday: 172 units
Sunday: 163 units
They find the total number of units sold throughout the week, which is 798 units, and divide the total by seven to get an average of 114 units sold.
With this information, the manager determines that the third store is performing the best and requires the most inventory space. The first and second stores require additional staff training and other changes to ensure an increase in sales throughout the week.
3. Determining the number of students in each class
A high school principal is planning class arrangements for each grade in the school. The principal wants to ensure that there is a balanced ratio between students and teachers to ensure the effectiveness of learning in each class and that teachers can safely monitor their students. According to student records, the principal gets the following number of students in each grade:
Grade nine: 452 students
Grade ten: 361 students
Grade 11: 521 students
Grade 12: 302 students
According to employment records, the principal gets the following number of teachers that specialize in each grade:
Grade nine: 15 teachers
Grade ten: 11 teachers
Grade 11: 16 teachers
Grade 12: 8 teachers
Based on this information, the principal determines the following number of classes per grade the number of students in each class:
There are 15 classes in grade nine and each class has an average of 30 students.
There are 11 classes in grade ten and each class has an average of 32 students.
There are 16 classes in grade 11 and each class has an average of 32 students.
There are 8 grade 12 glasses and each class has an average of 37 students.
Useful applications of finding the mean in a work environment
Using the calculations to find the mean is useful in a variety of industries and workplace roles. Some of these include management, production, human resources, and research. There are also other values you can use to help you analyze datasets, such as median and mode, but mean is one of the midpoint values you might often require calculating and interpreting. Finding the mean can help you make more informed decisions about the direction of the company and whether your business has enough resources to operate in a healthy and successful way.
Here are some of the scenarios where you may require finding the mean from a list of data:
1. Finding industry standards of assigning salaries
When managers and the human resource department assign salaries to a new hire or an existing employee promoted to a new role, it's helpful to understand what the industry average salary is for that role. Especially if you are creating a new role, having information about the average salary can help you determine appropriate remuneration for the employee. You can gather salary information from within the company or from external sources. This ensures you are paying a fair amount of compensation according to industry standards and allocating enough budget to these salaries.
2. Managing investment portfolios
Although there are many complex calculations involved in managing a healthy investment portfolio, financial advisors can use the mean formula to calculate the average yearly return of their client portfolios, portfolio management expenses, change in volatility, and portfolio risk. You can also determine the average amount of money your clients invest into their portfolios each month throughout a one-year period. This information helps you determine whether your clients are on track to meet their investment goals. It also helps your clients understand a part of their financial circumstances, which is beneficial when making decisions about large purchases.
3. Setting prices of your products
Setting your prices correctly is essential for attracting enough customers to help your business succeed and sustain operations. If you price your products too low, you can lose profit margins from each sale. If you price your products too high, you might not be able to attract as many customers as your competitors. Calculating and comparing average prices for similar products in the market from different brands and locations can help you set a reasonable price for your products and services that customers can pay and give your business the target profit margin of the organization.
4. Making purchases from vendors
Many businesses make purchases from external vendors and business partners, especially supply chains and manufacturers. Calculating the average price of the materials you require can help you determine how much money you are spending and if you are paying a fair price. If an item costs more than the average price of the materials you source, then you may consider changing the vendor.
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