Arithmetic mean

3 key takeaways

• The arithmetic mean is the sum of all values in a dataset divided by the number of values.
• It provides a simple measure of the central tendency of a dataset.
• The arithmetic mean is sensitive to extreme values (outliers), which can skew the result.

What is the arithmetic mean?

The arithmetic mean is a statistical measure used to calculate the central value of a dataset. It is obtained by summing all the numbers in a dataset and then dividing by the number of values in that dataset. This measure is widely used in various fields, including finance, economics, and social sciences, to represent the average value.

Importance of the arithmetic mean

The arithmetic mean is important because it provides a single value that summarizes the characteristics of an entire dataset. It is easy to calculate and understand, making it a fundamental tool for data analysis and interpretation. However, it is essential to consider the presence of outliers, as they can disproportionately affect the mean, leading to potentially misleading conclusions.

How the arithmetic mean works

Calculation: To calculate the arithmetic mean, follow these steps:

1. Sum all the values in the dataset.
2. Count the number of values in the dataset.
3. Divide the sum by the count of values.

Formula: Arithmetic Mean=∑????=1????????????????Arithmetic Mean=n∑i=1n​xi​​ where ∑????=1????????????∑i=1n​xi​ represents the sum of all values in the dataset, and ????n is the number of values.

Examples of the arithmetic mean

• Test scores: If a student receives the following scores in five tests: 80, 85, 90, 75, and 95, the arithmetic mean score is calculated as: Mean=80+85+90+75+955=4255=85Mean=580+85+90+75+95​=5425​=85
• Daily temperatures: Suppose the daily temperatures over a week are 70°F, 72°F, 68°F, 75°F, 74°F, 73°F, and 71°F. The arithmetic mean temperature for the week is: Mean=70+72+68+75+74+73+717=5037≈71.86 °FMean=770+72+68+75+74+73+71​=7503​≈71.86°F

Real-world application

Consider a scenario where a company wants to determine the average sales per month over a year. The monthly sales figures (in thousands) are: 120, 130, 125, 140, 135, 150, 145, 155, 160, 165, 170, and 175. The arithmetic mean sales figure is calculated as: Mean=120+130+125+140+135+150+145+155+160+165+170+17512=187012≈155.83 thousandsMean=12120+130+125+140+135+150+145+155+160+165+170+175​=121870​≈155.83thousands

This calculation provides the company with an average monthly sales figure, helping them understand typical sales performance and plan future strategies accordingly.

Understanding the arithmetic mean is crucial for summarizing and analyzing data effectively. It provides a quick and straightforward way to gauge the central value of a dataset, which is essential in various analytical and decision-making processes.

Related topics you might want to learn about include median, mode, and measures of central tendency. These areas provide further insights into different ways to summarize and interpret data distributions.