The coefficient of variation and standard deviation of an ungrouped data are 60 and 21 respectively. If 15 is added to every observation of the data, then the coefficient of variation of the new data is

Step-by-step solution

According to the given information, Coefficient of variance ( CV )= 100 Where is standard deviation and is mean of an ungrouped data. 100=60 and =21 So, = 21 10 6 =35 After adding 15 to each observation of the data, the new mean ^ =35+15=50 but | ^ -x_i^ |= | -x_i | , [where x_i^ =x_i+15 ] Now, = ( -x_i )^2 n =21 ( -x_i )^2=(21)^2 n So, new standard deviation ^ = ( ^ -x_i^ )^2 n = (21)^2 n n =21 New coefficient of variance = ^ ^ 100= 21 50 100=21 2=42 Hence, option (b) is correct.