To find the fourth seasonal index when three seasonal indices are given, you can use the principle that the sum of the seasonal indices for all periods (quarters, in this case) should equal the number of quarters.
Given the three seasonal indices:
- First quarter: 0.7
- Second quarter: 1.14
- Third quarter: 0.81
Let's denote the fourth seasonal index as \( S_4 \).
The sum of these indices should equal \( n \), where \( n \) is the number of quarters (which is 4 for quarterly data). Therefore:
\[ 0.7 + 1.14 + 0.81 + S_4 = 4 \]
Calculating the sum of the known indices:
\[ 0.7 + 1.14 + 0.81 = 2.65 \]
Now, substituting this into the equation:
\[ 2.65 + S_4 = 4 \]
To find \( S_4 \), subtract 2.65 from 4:
\[ S_4 = 4 - 2.65 = 1.35 \]
Thus, the fourth seasonal index is 1.35.