A survey recorded the daily pocket money (in rupees) received by 50 students. The data were compiled as a cumulative frequency distribution, shown below:
Pocket money (rupees) Less than 10 Less than 20 Less than 30 Less than 40 Less than 50
Cumulative frequency 8 19 32 45 50
Use this information to answer the following.
(i) Convert the cumulative frequencies into a regular frequency distribution table with class intervals 0–10, 10–20, 20–30, 30–40 and 40–50.
(ii) Using the table obtained in part (i), compute the mean daily pocket money, the variance and the standard deviation of the distribution (correct to the nearest rupee where necessary).