Final answer:
The question inquires about the calculation of mean, median, and mode for grouped data represented by class intervals and frequencies. To approximate the mean, midpoints of classes are used, while the median is found using cumulative frequencies, and the mode is identified by the highest frequency class.
Step-by-step explanation:
The student has asked to find the mean, median, and mode of the provided data set with class intervals and corresponding frequencies. The data set represents values that fall into different class intervals, and each interval has a frequency that indicates how many values fall within it.
Calculation of Mean
To approximate the mean for grouped data, we find the midpoint of each class by adding the lower and upper boundaries and dividing by two. Then, we multiply each midpoint by the frequency of that class, sum all of these products, and finally divide by the total frequency.
Calculation of Median
The median is the 50th percentile of the data, representing the middle value when the data is ordered. For grouped data, we would use the cumulative frequency distribution to determine the median class, then apply the formula to find the exact median value.
Calculation of Mode
The mode is the most frequently occurring data value in the dataset. In the case of grouped data, the modal class is the interval with the highest frequency.