Quick Math Mean
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Example (dataset): 5, 7, 8, 9 105, 7, 8, 9, 10
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Mean in Statistics
The mean is a measure of central tendency, often referred to as the “average” of a set of values. It is calculated by summing all the values in a dataset and then dividing by the number of values. The mean provides a single value that summarizes the general magnitude of the data.
Formula
For a dataset with values \( x_1, x_2, x_3, \ldots, x_n \), the mean \( \bar{x} \) is given by:
\[ \bar{x} = \frac{x_1 + x_2 + x_3 + \ldots + x_n}{n} \]
where:
– \( x_1, x_2, x_3, \ldots, x_n \) are the individual data points.
– \( n \) is the total number of data points.
Example
Let’s consider the following dataset representing the scores of students in a math test:
\[ 75, 80, 85, 90, 95 \]
To find the mean score:
1. Sum the values:
\[ 75 + 80 + 85 + 90 + 95 = 425 \]
2. Count the number of values:
There are 5 values in the dataset.
3. Calculate the mean:
\[ \bar{x} = \frac{425}{5} = 85 \]
So, the mean score of the students in the math test is 85.
This example illustrates how to calculate the mean and provides a simple, clear process for summarizing a set of data with a single representative value.