The correct answer is (a) 26.5.
To find the arithmetic mean, we first need to find the sum of the values in each class interval. We can do this by multiplying the frequency of each interval by the midpoint of the interval. The midpoint of each interval is calculated by taking the average of the upper and lower limits of the interval.
For example, the midpoint of the interval 0-10 is (0+10)/2 = 5.
Once we have the sum of the values in each class interval, we can calculate the arithmetic mean by dividing the sum by the total frequency.
The total frequency is the sum of the frequencies of all the intervals. In this case, the total frequency is 4+13+18+96 = 121.
The arithmetic mean is therefore:
(45)+(1315)+(1825)+(9635) / 121
= 26.5
The other options are incorrect because they do not represent the arithmetic mean of the data.