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Sagot :
To determine which city's data set is bimodal, we should examine each city's temperature data set and look for bimodal distributions, which are distributions with two different modes that occur with the highest frequency.
### Analyzing each city:
1. City A:
- Temperatures: \(10, 12, 10, 14, 15, 16, 21, 14, 28, 10, 21, 22\)
- Frequency count:
\(10 \to 3\),
\(12 \to 1\),
\(14 \to 2\),
\(15 \to 1\),
\(16 \to 1\),
\(21 \to 2\),
\(28 \to 1\),
\(22 \to 1\)
- The highest frequency is \(3\) (occurs for temperature \(10\)). The second highest frequency is \(2\) (occurs for temperatures \(14\) and \(21\)).
- Since it does not have two distinct values sharing the highest frequency, the data set for City A is not bimodal.
2. City B:
- Temperatures: \(25, 38, 27, 25, 26, 37, 29, 25, 30, 25, 25, 27\)
- Frequency count:
\(25 \to 5\),
\(38 \to 1\),
\(27 \to 2\),
\(26 \to 1\),
\(37 \to 1\),
\(29 \to 1\),
\(30 \to 1\)
- The highest frequency is \(5\) (occurs for temperature \(25\)). The second highest frequency is \(2\) (occurs for temperature \(27\)).
- Since it does not have two distinct values sharing the highest frequency, the data set for City B is not bimodal.
3. City C:
- Temperatures: \(43, 42, 39, 42, 41, 53, 62, 66, 66, 38, 42, 66\)
- Frequency count:
\(43 \to 1\),
\(42 \to 3\),
\(39 \to 1\),
\(41 \to 1\),
\(53 \to 1\),
\(62 \to 1\),
\(66 \to 3\),
\(38 \to 1\)
- The highest frequency is \(3\) (occurs for temperatures \(42\) and \(66\)).
- Since the highest frequency is \(3\) for both \(42\) and \(66\), the data set for City C is bimodal.
4. City D:
- Temperatures: \(53, 56, 78, 70, 76, 53, 78, 78, 73, 72, 68, 68\)
- Frequency count:
\(53 \to 2\),
\(56 \to 1\),
\(78 \to 3\),
\(70 \to 1\),
\(76 \to 1\),
\(73 \to 1\),
\(72 \to 1\),
\(68 \to 2\)
- The highest frequency is \(3\) (occurs for temperature \(78\)). The second highest frequency is \(2\) (occurs for temperatures \(53\) and \(68\)).
- Since it does not have two distinct values sharing the highest frequency, the data set for City D is not bimodal.
### Conclusion:
Only City C has a bimodal distribution, with temperatures \(42\) and \(66\) both occurring the highest number of times (3 times each).
Therefore, the answer is:
C) City C
### Analyzing each city:
1. City A:
- Temperatures: \(10, 12, 10, 14, 15, 16, 21, 14, 28, 10, 21, 22\)
- Frequency count:
\(10 \to 3\),
\(12 \to 1\),
\(14 \to 2\),
\(15 \to 1\),
\(16 \to 1\),
\(21 \to 2\),
\(28 \to 1\),
\(22 \to 1\)
- The highest frequency is \(3\) (occurs for temperature \(10\)). The second highest frequency is \(2\) (occurs for temperatures \(14\) and \(21\)).
- Since it does not have two distinct values sharing the highest frequency, the data set for City A is not bimodal.
2. City B:
- Temperatures: \(25, 38, 27, 25, 26, 37, 29, 25, 30, 25, 25, 27\)
- Frequency count:
\(25 \to 5\),
\(38 \to 1\),
\(27 \to 2\),
\(26 \to 1\),
\(37 \to 1\),
\(29 \to 1\),
\(30 \to 1\)
- The highest frequency is \(5\) (occurs for temperature \(25\)). The second highest frequency is \(2\) (occurs for temperature \(27\)).
- Since it does not have two distinct values sharing the highest frequency, the data set for City B is not bimodal.
3. City C:
- Temperatures: \(43, 42, 39, 42, 41, 53, 62, 66, 66, 38, 42, 66\)
- Frequency count:
\(43 \to 1\),
\(42 \to 3\),
\(39 \to 1\),
\(41 \to 1\),
\(53 \to 1\),
\(62 \to 1\),
\(66 \to 3\),
\(38 \to 1\)
- The highest frequency is \(3\) (occurs for temperatures \(42\) and \(66\)).
- Since the highest frequency is \(3\) for both \(42\) and \(66\), the data set for City C is bimodal.
4. City D:
- Temperatures: \(53, 56, 78, 70, 76, 53, 78, 78, 73, 72, 68, 68\)
- Frequency count:
\(53 \to 2\),
\(56 \to 1\),
\(78 \to 3\),
\(70 \to 1\),
\(76 \to 1\),
\(73 \to 1\),
\(72 \to 1\),
\(68 \to 2\)
- The highest frequency is \(3\) (occurs for temperature \(78\)). The second highest frequency is \(2\) (occurs for temperatures \(53\) and \(68\)).
- Since it does not have two distinct values sharing the highest frequency, the data set for City D is not bimodal.
### Conclusion:
Only City C has a bimodal distribution, with temperatures \(42\) and \(66\) both occurring the highest number of times (3 times each).
Therefore, the answer is:
C) City C
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