To determine the mode of the data distributions for January temperatures in the two years, we first need to identify the mode for each year's data.
For 2021: The temperatures are: 35, 48, 32, 40, 38, 34, 35, 35, 32, 36, 32, 39, 35
The mode is the value that appears most frequently. In 2021, the temperature 35 appears four times, while all other temperatures appear less frequently. Thus, the mode for 2021 is 35.
For 2022: The temperatures are: 51, 50, 30, 31, 41, 37, 31, 29, 36, 36, 19, 34, 44
In 2022, the temperatures of 31 and 36 both appear twice, and no other temperature appears as frequently. Therefore, the modes for 2022 are 31 and 36.
Using this analysis, we can evaluate the provided statements:
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The mode in 2021 is 35 and it is 31 and 36 in 2022, indicating the temperatures deviated little between these two years.
- This statement is partially correct for the modes, but it incorrectly interprets the significance of the mode.
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The mode in 2021 is 36.2, and it is 36 in 2022, indicating the temperatures are staying the same from year to year.
- This statement is incorrect. The mode in 2021 is not 36.2; it's 35.
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The mode in 2021 is 35, and it is 31 and 36.1 in 2022, indicating that temperatures are getting colder each year.
- This statement is incorrect. While it correctly identifies the mode in 2021, it wrongly states the mode for 2022 as 36.1; it is actually 31 and 36.
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The mode in 2021 is 32, and it is 19 in 2022, indicating temperatures are getting colder.
- This statement is incorrect as the mode for 2021 is not 32.
In summary, the most accurate statement based on the analysis is the first one: "The mode in 2021 is 35 and it is 31 and 36 in 2022..." but it should be noted that while this statement acknowledges that the modes are different, it does not indicate whether the temperatures are getting colder or what the actual differences signify.