Match List-I with List-II
| List-I | List-II | ||
| (A) | Method of moving averages | (I) | Makes \(\sum X = 0\) |
| (B) | Method of least squares | (II) | Needed when the period of the moving average is even |
| (C) | Centring of moving averages | (III) | Used mostly to smooth out seasonal variations |
| (D) | Taking the middle year as the origin | (IV) | Makes \(\sum (y - y_t)^2\) least |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A)-(III), (B)-(IV), (C)-(II), (D)-(I)
Each item is a tool used in measuring the trend of a time series.
(A) Method of moving averages
This matches (III) Used mostly to smooth out seasonal variations: averaging consecutive values removes the short-term ups and downs and leaves a smooth trend curve.
(B) Method of least squares
This matches (IV) Makes \(\sum (y - y_t)^2\) least: the fitted line is the one with the least sum of squares of the deviations.
(C) Centring of moving averages
This matches (II) Needed when the period of the moving average is even: an even-period average falls between two years, and centring brings it against an actual year.
(D) Taking the middle year as the origin
This matches (I) Makes \(\sum X = 0\): the X values lie symmetrically about 0, so they cancel.