Arithmetic Mean

Arithmetic mean also known as average. Arithmetic Mean for a given set of data is calculated by adding up the numbers in the data and dividing the sum so obtained with the number of observations. It is the most popular method of central tendency.

Properties of Arithmetic Mean

• Deviations from the arithmetic mean of all items in a statistical series would always add up to zero, i.e. ∑(x – X) = 0.
• The squared deviations from the arithmetic mean is always minimum, i.e., less than the sum of such square deviations from other values like the median, mode, or another tool.
• Replacing all the items in a statistical series with its arithmetic mean has no effect on the sum of the said items.

Using Direct Method

The arithmetic mean is calculated using the following formula,

Sum of observation/Number of observations

Mean of the series = x̄ = Σx/ N.

The formula discussed above pertains to the direct method of calculating the arithmetic mean. But in the case where the calculation becomes tedious owing to larger observations in a data set, other methods can be used to calculate the arithmetic mean, one of such methods being the step-deviation method. 

Read More

• Find group of mean data using direct method

The Step Deviation Method is a simplified way to calculate the mean of a grouped frequency distribution, especially when the class intervals are uniform. In simple words, statistics implies the process of gathering, sorting, examine, interpret and then present the data in an understandable manner so as to enable one to form an opinion of it and take necessary action, if necessary. Examples:

• A teacher collecting students’ marks, organizing them in ascending or descending manner, and calculating the average class marks, or finding the number of students who failed, informing them so that they start working hard.

• Government officials collecting data for the census, and comparing it with previous records to see whether population growth is in control or not.

• Analyzing the number of followers of a particular religion of a country.