(a) Compute the weighted arithmetic mean of the indices of various groups as given below:
(b) A cumulative frequency distribution has 65 as the mid-value of its last class interval. The cumulative frequencies of the first, second ...... seventh classes are 5, 21, 45, 72, 85, 94 and 100 respectively. If all the class intervals are of equal width of 10 units, write down the relevant frequency distribution. Also calculate its mean and median.