Calculating the Mean in Statistics

Calculating the Mean

• The mean is a measure of central tendency that represents the average of a dataset.
• The mean can be calculated for both individual data points and grouped data.
• To calculate the mean of individual data points, sum all the values and divide by the total number of values.
• For grouped data, the mean is calculated using the formula: $y = \frac{\sum{fiyi}}{\sum fi}$, where $fi$ is the frequency of each interval and $yi$ is the midpoint of each interval.
• Finding the midpoint of each interval is crucial for calculating the mean of grouped data.
• Multiplying the frequency of each interval by its midpoint provides the value for ($fi \times yi$).
• Summing the values of ($fi \times yi$) gives the value of $\sum{fiyi}$.
• Similarly, sum all the frequencies to get the value of $\sum{fi}$.
• The mean is then calculated by dividing the sum of ($fi \times yi$) by the sum of frequencies.
• In the provided example, the mean of the grouped data is calculated to be approximately 186.67.