GATE2014 AE: GA-10

Question

The monthly rainfall chart based on $50$ years of rainfall in Agra is shown in the following figure.

Which of the following are true? (k percentile is the value such that k percent of the data fall below that value)

1. On average, it rains more in July than in December
2. Every year, the amount of rainfall in August is more than that in January
3. July rainfall can be estimated with better confidence than February rainfall
4. In August, there is at least $500$ mm of rainfall

• A. (i) and (ii)
• B. (i) and (iii)
• C. (ii) and (iii)
• D. (iii) and (iv)

Answer 1

1st statement true since average of July is more than that of December in the Average plot

2nd statement - not true since, we have data till $95\%$ only -- in all data of $50$ years, amount of rainfall is below the value presented by graph in $95\%$ cases. So in the remaining $5\%$ of years, there can be a year where it rains more in January than August

3rd statement true- since difference between $5-\text{percentile}$ plot and $95-\text{percentile}$ plot indicates that this was range for $90\%$ of years. In February this range is bigger compared to July.

4th statement - not necessarily true. Here, the $5-\text{percentile}$ plot is touching $500mm$ level. But any year in this $5\%$ could have got a lower level of rainfall.

So, answer is $B.$

Comments

For 2nd statement: It is not necessary that every year Aug rainfall is more than Jan.

As if for some year Aug rainfall is very high and Jan rainfall is very low then also Aug average could be more than Jan.

Same for 4th statement.