Precipitation MCQ with answer and solution

Concept

Estimation of Missing Rainfall Data

Formula

Arithmetic Mean Method: Px = (P1 + P2 + ... + Pm) / m Normal Ratio Method: Px = (Nx / m) × (P1/N1 + P2/N2 + ... + Pm/Nm)

Step-by-step solution

1. Identify the criteria for selecting between the Arithmetic Mean Method and the Normal Ratio Method for estimating missing rainfall data. 2. Recall that the Arithmetic Mean Method is applied when surrounding station normal precipitation values are within 10% of the missing station, whereas the Normal Ratio Method is used when they differ by more than 10%. 3. Observe that both statements in the question have swapped these conditions, making both statements incorrect, and select Option (d) as the correct choice.

Explanation

Both statements are incorrect because the conditions for the two methods are swapped. The Arithmetic Mean method is used when the normal precipitation of surrounding stations is within 10% of the missing station's normal precipitation, whereas the Normal Ratio method is used when the difference is greater than 10%.

Shortcut

To easily remember the missing rainfall data methods, use the rule "Average for Close, Ratio for Far": - Within 10% (Close): Use Arithmetic Mean Method (simple average when values are nearly equal). - Exceeds 10% (Far/Different): Use Normal Ratio Method (uses normal ratios to adjust for larger variations).

Common mistake

A common mistake is selecting Option C (Both 1 and 2) by confusing or swapping the criteria for the two methods. Students often forget that the Arithmetic Mean method is used when the normal annual precipitation of surrounding stations is within 10% of the missing station, whereas the Normal Ratio method is applied when the variation exceeds 10%. Because the statements in the question swap these conditions, both statements are incorrect, making Option D the correct choice.