The analysis of the results of a budget survey of 150 families gave an average monthly expenditure of Rs. 120 on food items with a standard deviation of Rs. 15. After the analysis was completed it was noted that the figure recorded for one household was wrongly taken as Rs. 15 instead of Rs. 105. Determine the correct value of the average expenditure and its standard deviation.

Question: The analysis of the results of a budget survey of 150 families gave an average monthly expenditure of Rs. 120 on food items with a standard deviation of Rs. 15. After the analysis was completed it was noted that the figure recorded for one household was wrongly taken as Rs. 15 instead of Rs. 105. Determine the correct value of the average expenditure and its standard deviation.

Solution:

A.M. (x) = Rs. 120, No. of items = 150
Total as obtained = 120 x 150 = 18000
Correct total = (Total obtained – item misread) + correct item
= (18000-15) + 105 = 18,090
Correct mean = Correct total/No. of items = 18090/150
= Rs. 120.6

correct sd is 12.4