Actual Mean Method to Calculate Standard Deviation
The marks of ...
Question
The marks of some students were listed from total marks of 75. The standard deviation of marks was found to be 9. Subsequently, the marks were raised to a maximum of 100, and variance of new marks was calculated. The new variance is
A
81
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
122
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
144
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
196
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is C144 Given : σ=9 Let a student obtains X marks out of 75. Then his/her marks out of 100 is 10075X=43X
So, each observation should be multiplied by 43 for obtaining new data set. Hence, new variance =(43)2×92=144