The weekly wages (in ₹) of 100 factory workers were recorded in the following form:
Wages (₹) | Below 100 | 100–120 | 120–140 | 140–160 | 160–180 | 180 and above
Number of workers | 8 | 12 | 25 | 30 | 18 | 7
(i) Explain clearly why the arithmetic mean wage cannot be determined exactly from the above distribution.
(ii) Modify the first and the last class such that all class intervals have equal width of ₹20, taking the lower limit of the first class as ₹80. Write the amended continuous grouped distribution.
(iii) Using the amended distribution of part (ii), calculate the median wage of the workers.
(iv) State one limitation of the median value obtained in part (iii) with reference to the assumptions you made in part (ii).