CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If a is added to all the observations, (where a can be either positive or negative integer) then what is the relation between the old and new variance.
(Old variance =σ2 and New variance =σ2)

A
σ2=a×σ2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
σ2=a2×σ2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
σ2=σ2a
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
σ2=σ2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D σ2=σ2
Let Mean be u=xin
Let yi=xi+a for all i=1,2,3....n.
Now new Mean, u=yin
Now new Mean, u=(xi+a)n
u=u+a.
Now, variance, σ2=1n×(yiu)2
σ2=1n×((xi+a)(u+a))2
σ2=1n×(xiu)2=σ2
Thus, σ2=σ2
Ans-Option D

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Mean Deviation about Mean
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon