The formula to calculate the mean for grouped data is:
\[ \bar{x} = \frac{\sum (f \cdot m)}{\sum f} \]
Where:
Central tendency in grouped data refers to the measure that identifies the center of a data set. It is a way to summarize a set of data by identifying the central position within that set of data. The most common measures of central tendency are the mean, median, and mode. For grouped data, these measures are calculated using the frequencies and midpoints of the classes. The mean is particularly useful as it takes into account all data points and provides a single value that represents the entire data set.
Let's assume the following values:
Using the formula:
\[ \bar{x} = \frac{(5 \cdot 2) + (10 \cdot 4) + (15 \cdot 6)}{5 + 10 + 15} = \frac{10 + 40 + 90}{30} = \frac{140}{30} = 4.67 \]
The mean is 4.67.
