Final answer:
The true statement among the given options is A) The mode is always one of the numbers in a data, which is due to the definition of mode as the most frequently occurring number(s) in a data set.
Step-by-step explanation:
When considering the statement 'which of the following is true?' related to mean, median, and mode, it's important to understand the definitions of these terms:
- The mean is the sum of all numbers in a data set divided by the count of the numbers.
- The median is the middle value when the data set is ordered from least to greatest.
- The mode is the most frequently occurring number(s) in a data set.
Statement A is correct: The mode is always one of the numbers in a data. This is because by definition, the mode is the number that appears most frequently in a data set. Therefore, it must be a number that exists in the set.
Statement B is incorrect because the mean is an average, which might not be a number that actually exists in the data set. Statements C and D are incorrect because they present false generalizations. The relationships between mean, median, and mode depend on the distribution of the data. For example, in a symmetrical distribution, the mean, median, and mode are all equal. However, if the distribution is skewed, these values can differ significantly.
In conclusion, A) The mode is always one of the numbers in a data is the true statement among the options provided.