Study the table and answer the question that follows.
Year State 2000 2005 2015 Himachal Pradesh 110 90 150 Uttar Pradesh 120 85 90 Madhya Pradesh 90 65 80 Andhra Pradesh 55 75 65 Tamil Nadu 150 90 115
Analyzing Rainfall Data Table
The question asks to identify the state where the annual rainfall in 2005 exceeded the average annual rainfall calculated across the years 2000, 2005, and 2015 for that specific state. We need to calculate the average rainfall for each state and compare it with the 2005 rainfall.
| Year | 2000 | 2005 | 2015 |
| Himachal Pradesh | 110 | 90 | 150 |
| Uttar Pradesh | 120 | 85 | 90 |
| Madhya Pradesh | 90 | 65 | 80 |
| Andhra Pradesh | 55 | 75 | 65 |
| Tamil Nadu | 150 | 90 | 115 |
Calculating Average Rainfall Per State
The average annual rainfall for each state is calculated using the formula:
$ \text{Average Rainfall} = \frac{\text{Rainfall}_{2000} + \text{Rainfall}_{2005} + \text{Rainfall}_{2015}}{3} $
Let's calculate the average for each state:
- Himachal Pradesh: $ \frac{110 + 90 + 150}{3} = \frac{350}{3} \approx 116.67 \text{ cm} $
- Uttar Pradesh: $ \frac{120 + 85 + 90}{3} = \frac{295}{3} \approx 98.33 \text{ cm} $
- Madhya Pradesh: $ \frac{90 + 65 + 80}{3} = \frac{235}{3} \approx 78.33 \text{ cm} $
- Andhra Pradesh: $ \frac{55 + 75 + 65}{3} = \frac{195}{3} = 65 \text{ cm} $
- Tamil Nadu: $ \frac{150 + 90 + 115}{3} = \frac{355}{3} \approx 118.33 \text{ cm} $
Comparing 2005 Rainfall with Average
Now, we compare the rainfall in 2005 for each state with its calculated average annual rainfall:
- Himachal Pradesh: 2005 Rainfall (90 cm) is NOT greater than Average (116.67 cm).
- Uttar Pradesh: 2005 Rainfall (85 cm) is NOT greater than Average (98.33 cm).
- Madhya Pradesh: 2005 Rainfall (65 cm) is NOT greater than Average (78.33 cm).
- Andhra Pradesh: 2005 Rainfall (75 cm) IS greater than Average (65 cm).
- Tamil Nadu: 2005 Rainfall (90 cm) is NOT greater than Average (118.33 cm).
The state where the annual rainfall for 2005 was greater than the average annual rainfall for all three years is Andhra Pradesh.
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