Calculating the Mean in Statistics

The mean of the provided weights is approximately $186.67$.

The formula used for calculating the mean of grouped data is $y = \frac{\sum{fiyi}}{\sum{fi}}$.

The midpoint of the weight range 101-150 grams is $125.5$.

The sum of frequencies for the given data is $100$.

The sum of $(fi \times yi)$ for the weight intervals equals $14000$.

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.

This quiz focuses on the concept of mean, a key measure of central tendency in statistics. You will learn how to calculate the mean for both individual and grouped data, including the necessary formulas and steps. Test your understanding of finding midpoints and using frequency in calculations.