If 18, Q, 19.2, T, 19.8 are the 5-year moving averages of the following series of observations:
16, P, 20, 18, R, 17, 19, S, 20, then
Match List-I with List-II
| List-I | List-II | ||
| (A) | \( 3P+2R \) | (I) | 11.4 |
| (B) | \( 2R-(P+S) \) | (II) | 86 |
| (C) | \( \displaystyle\frac{1}{5}(P+R+S) \) | (III) | 37.6 |
| (D) | \( Q+T \) | (IV) | 9 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A) - (II), (B) - (IV), (C) - (I), (D) - (III)
Nine observations give five 5-year moving averages: terms 1-5, 2-6, 3-7, 4-8 and 5-9. So 18, 19.2 and 19.8 are the averages of terms 1-5, 3-7 and 5-9, and Q, T are the averages of terms 2-6 and 4-8.
\( \displaystyle \frac{16+P+20+18+R}{5}=18 \)
\( \displaystyle P+R=36 \)
\( \displaystyle \frac{20+18+R+17+19}{5}=19.2 \)
\( \displaystyle R=96-74=22 \)
so P = 14.
\( \displaystyle \frac{R+17+19+S+20}{5}=19.8 \)
\( \displaystyle S=99-78=21 \)
\( \displaystyle Q=\frac{14+20+18+22+17}{5} \)
\( \displaystyle =18.2 \)
\( \displaystyle T=\frac{18+22+17+19+21}{5} \)
\( \displaystyle =19.4 \)
(A) \( 3P+2R \)
This matches (II) 86: \( 3(14)+2(22)=42+44=86 \).
(B) \( 2R-(P+S) \)
This matches (IV) 9: \( 2(22)-(14+21)=44-35=9 \).
(C) \( \frac{1}{5}(P+R+S) \)
This matches (I) 11.4: \( \frac{1}{5}(14+22+21)=\frac{57}{5}=11.4 \).
(D) \( Q+T \)
This matches (III) 37.6: \( 18.2+19.4=37.6 \).
So the matching is (A)-(II), (B)-(IV), (C)-(I), (D)-(III).