The following table shows the amount of annual rainfall in inches in 8 different states of India. T A M N K P D R 2015 80 70 98 78 68 65 70 59 2016 85 70 95 77 69 60 71 59 2017 86 71 96 76 66 67 71 59 2018 84 70 96 75 67 66 69 61 2019 80 74 97 74 67 64 75 60 2020 81 75 98 75 68 65 74 65 2021 82 72 98 73 70 65 73 65 How many states have witnessed an increase in the amount of annual rainfall continuously for two times in immediate years?
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Understanding Annual Rainfall Trends in Indian States
The question asks us to identify the number of states that experienced a continuous increase in annual rainfall for two consecutive years within the period from 2015 to 2021. This means we are looking for a sequence of three immediate years where the rainfall in the second year was greater than the first, and the rainfall in the third year was greater than the second.
Annual Rainfall Data (2015-2021)
Here is the provided annual rainfall data for 8 states (T, A, M, N, K, P, D, R) over the years 2015 to 2021:
| State | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 |
|---|---|---|---|---|---|---|---|
| T | 80 | 85 | 86 | 84 | 80 | 81 | 82 |
| A | 70 | 70 | 71 | 70 | 74 | 75 | 72 |
| M | 98 | 95 | 96 | 96 | 97 | 98 | 98 |
| N | 78 | 77 | 76 | 75 | 74 | 75 | 73 |
| K | 68 | 69 | 66 | 67 | 67 | 68 | 70 |
| P | 65 | 60 | 67 | 66 | 64 | 65 | 65 |
| D | 70 | 71 | 71 | 69 | 75 | 74 | 73 |
| R | 59 | 59 | 59 | 61 | 60 | 65 | 65 |
Criteria for Continuous Rainfall Increase
We need to find states where the annual rainfall showed an increasing trend for two consecutive years. For example, if the rainfall in 2016 was higher than in 2015, AND the rainfall in 2017 was higher than in 2016, this state meets the criteria for the period 2015-2017. We check all possible two-year consecutive increase periods within the 2015-2021 range:
- Increase from 2015 to 2016 AND 2016 to 2017
- Increase from 2016 to 2017 AND 2017 to 2018
- Increase from 2017 to 2018 AND 2018 to 2019
- Increase from 2018 to 2019 AND 2019 to 2020
- Increase from 2019 to 2020 AND 2020 to 2021
A state qualifies if it shows at least one such sequence of two immediate years of continuous rainfall increase.
State-wise Rainfall Trend Analysis
Let's examine each state's rainfall data to identify periods of continuous increase over two immediate years:
- State T:
- 2015-2017: 80 < 85 < 86. Yes (Increase 2015->2016 and 2016->2017).
- 2016-2018: 85, 86, 84. No (84 is not > 86).
- 2017-2019: 86, 84, 80. No.
- 2018-2020: 84, 80, 81. No.
- 2019-2021: 80 < 81 < 82. Yes (Increase 2019->2020 and 2020->2021).
- State A:
- 2015-2017: 70, 70, 71. No (70 is not > 70).
- 2016-2018: 70, 71, 70. No.
- 2017-2019: 71, 70, 74. No.
- 2018-2020: 70 < 74 < 75. Yes (Increase 2018->2019 and 2019->2020).
- 2019-2021: 74, 75, 72. No.
- State M:
- 2015-2017: 98, 95, 96. No.
- 2016-2018: 95, 96, 96. No.
- 2017-2019: 96, 96, 97. No.
- 2018-2020: 96 < 97 < 98. Yes (Increase 2018->2019 and 2019->2020).
- 2019-2021: 97, 98, 98. No.
- State N:
- 2015-2017: 78, 77, 76. No.
- 2016-2018: 77, 76, 75. No.
- 2017-2019: 76, 75, 74. No.
- 2018-2020: 75, 74, 75. No.
- 2019-2021: 74, 75, 73. No.
- State K:
- 2015-2017: 68, 69, 66. No.
- 2016-2018: 69, 66, 67. No.
- 2017-2019: 66, 67, 67. No.
- 2018-2020: 67, 67, 68. No.
- 2019-2021: 67 < 68 < 70. Yes (Increase 2019->2020 and 2020->2021).
- State P:
- 2015-2017: 65, 60, 67. No.
- 2016-2018: 60, 67, 66. No.
- 2017-2019: 67, 66, 64. No.
- 2018-2020: 66, 64, 65. No.
- 2019-2021: 64, 65, 65. No.
- State D:
- 2015-2017: 70, 71, 71. No.
- 2016-2018: 71, 71, 69. No.
- 2017-2019: 71, 69, 75. No.
- 2018-2020: 69, 75, 74. No.
- 2019-2021: 75, 74, 73. No.
- State R:
- 2015-2017: 59, 59, 59. No.
- 2016-2018: 59, 59, 61. No.
- 2017-2019: 59, 61, 60. No.
- 2018-2020: 61, 60, 65. No.
- 2019-2021: 60, 65, 65. No.
Summary of Results
The states that witnessed an increase in the amount of annual rainfall continuously for two immediate years are State T, State A, State M, and State K.
Let's count these states:
- State T: Yes
- State A: Yes
- State M: Yes
- State N: No
- State K: Yes
- State P: No
- State D: No
- State R: No
There are 4 states that meet the specified criteria.
Conclusion
Based on the analysis of the annual rainfall data from 2015 to 2021, 4 states have witnessed an increase in the amount of annual rainfall continuously for two immediate years at least once during this period.
Revision Table: Key Learnings
| Concept | Explanation | Application to Problem |
|---|---|---|
| Data Analysis | Examining data points over time to find patterns. | Analyzing rainfall data year-by-year for each state. |
| Consecutive Increase | A value increasing from one period to the next, and then increasing again in the subsequent period. | Checking for Year X < Year X+1 < Year X+2 rainfall pattern. |
| Counting based on Criteria | Identifying how many items in a set meet a specific condition. | Counting the number of states with the continuous increase pattern. |
Additional Information: Rainfall Patterns and Climate Data
Analyzing annual rainfall data is crucial for understanding climate patterns and their impact on agriculture, water resources, and ecosystems. Rainfall can vary significantly from year to year due to various climatic factors, including monsoons, El Niño/La Niña cycles, and regional weather systems. Continuous increase or decrease over multiple years can indicate potential shifts in local or regional climate trends, although a longer dataset would be needed for definitive climate change conclusions. Data presented in tables like this helps in identifying trends, anomalies, and comparing performance across different regions.
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