Final answer:
The arithmetic mean of a frequency distribution can usually be calculated, but the question lacks the detailed mark ranges required for full calculation. Instead, one can estimate by assuming midpoints within class intervals, though this data is also missing from the question.
Step-by-step explanation:
The student is looking to calculate the arithmetic mean when given a frequency distribution of marks where each category represents the number of students achieving more than a certain score. The arithmetic mean or average is calculated by dividing the sum of all the values by the number of values.
To compute it from the given data, we need to know the actual marks corresponding to the given intervals. Since that is not provided, we are not able to calculate the mean directly. However, we can discuss methods of estimation such as assuming midpoints for each class interval when full data isn't available.
For example, if we had the intervals 0-10, 10-20, etc., we would take the midpoint of each interval, multiply it by the frequency of that interval, and divide the sum of these products by the total number of students to get an estimated mean.
To calculate the mean, multiply each value by its corresponding number of students, then add up the products. Finally, divide the sum by the total number of students.
Mean = (0*100 + 10*88 + 20*70 + 30*43 + 40*23 + 50*6) / (100 + 88 + 70 + 43 + 23 + 6)
Mean = 21.05