Latika Leekha
Last Activity: 10 Years ago
All the three statistical measures, mean, median and mode depend on absolaute values while variance measures spread of data points. Hence, if all the points are shifted by the same amount, the spread will not change and hence the variance remains the same. We show how the variance remains unchanged if the teacher gives grace marks of 10 to each student:
Let the original marks be xi, i = 1 to N.
Then, new marks are yi = xi + 10, i = 1 to N.
Let
be the original and new mean values.
Then, by definition, mean, N .
=
Similarly, N.
=
N.
= x
i + 10
Hence,
Now we try to find the original and new variance
Original variance, i.e. σ2org = [Σ (xi – mean)2] / N
New variance, i.e. σ2new = [Σ (yi – mean)2] / N
= Σ[(x
i + 10) – (
)]
2 / N
= Σ (xi – mean)2 / N
= σ2org
Hence, the two variance are the same.
Thanks & Regards
Latika Leekha
askIITians Faculty
