3.2:
Arithmetic Mean
Arithmetic mean is often used to average numerical data sets. It is calculated by adding all the values in the data set and dividing them by the total number of values, n. Here, the uppercase sigma indicates the sum of all the values.
For example, consider the daily screen time of students in a school. To find out the arithmetic mean, add up the screen time of all students and then divide the result by the total number of students.
The study sample involves only a few students selected at random. The mean of such sample data is called the sample mean, denoted by x bar.
Instead, if the data was collected from every student in the school, it becomes population data. The resulting population mean is denoted by mu.
Since arithmetic mean considers every data value, it is considered representative of the data. But, a single extreme value can significantly change the mean, making it a very sensitive measure of center.
3.2:
Arithmetic Mean
The arithmetic mean is the most commonly used measure of the central tendency of a data set. It is defined as the sum of all the elements constituting the data set, divided by the total number of elements. It is sometimes loosely referred to as the “average.”
When all the values in a data set are not unique, the sum in the numerator can be calculated by multiplying each distinct value by its frequency.
Sometimes, the arithmetic mean of a sample can be affected by a few data points that are significantly different from the rest, outliers. For example, if in a sample of ten students, nine students have ages varying 20 and 21 while one student is ten years old, then the arithmetic mean would be less than 20, which is not a true representation of the central tendency of the students’ ages. Hence, careful consideration is required before using the arithmetic mean to measure the central tendency of a data set.
The arithmetic mean of a qualitative data set cannot be calculated. For example, in a class of students with different nationalities, there is no arithmetic mean for nationality.