Final answer:
In calculating the arithmetic mean for grouped data, the midpoint of the class is used to represent all values in that class. It is found by averaging the lower and upper limits of the class interval and then multiplying by the class's frequency.The correct option that represents all the values in a particular class for the calculation of the arithmetic mean is thus d. The midpoint of the class.
Step-by-step explanation:
In the calculation of the arithmetic mean for grouped data, we do not know the individual values within each class. Therefore, we need a representative value for each class to estimate the mean. This representative value is the midpoint of the class,
which is calculated as the sum of the lower and upper limits of the class interval divided by two. To find the mean of a grouped frequency table, we multiply this midpoint by the frequency of the class and sum the results for all classes. Finally, we divide this sum by the total number of data values in the set to find the estimated mean.
The correct option that represents all the values in a particular class for the calculation of the arithmetic mean is thus d. The midpoint of the class.