Questions: Which of the following statements are TRUE? Check all that apply. The mode is the number (or numbers) that occurs most frequently in the set. The median is the number in the middle of a set of numbers arranged in numerical order. If no number or numbers occur more than once, the mode is zero. The mean is the average of all the data values.

Which of the following statements are TRUE? Check all that apply. The mode is the number (or numbers) that occurs most frequently in the set. The median is the number in the middle of a set of numbers arranged in numerical order. If no number or numbers occur more than once, the mode is zero. The mean is the average of all the data values.
Transcript text: Which of the following statements are TRUE? Check all that apply. The mode is the number (or numbers) that occurs most frequently in the set. The median is the number in the middle of a set of numbers arranged in numerical order. If no number or numbers occur more than once, the mode is zero. The mean is the average of all the data values.
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Solution

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Solution Steps

Step 1: Analyze the statement about the mode

The statement says: "The mode is the number (or numbers) that occurs most frequently in the set."
This is true. The mode is defined as the value(s) that appear most often in a dataset.

Step 2: Analyze the statement about the median

The statement says: "The median is the number in the middle of a set of numbers arranged in numerical order."
This is true. The median is the middle value when the data is sorted in ascending or descending order. If there is an even number of observations, the median is the average of the two middle numbers.

Step 3: Analyze the statement about the mode when no number repeats

The statement says: "If no number or numbers occur more than once, the mode is zero."
This is false. If no number repeats, the dataset has no mode, not a mode of zero. A dataset can have no mode, one mode, or multiple modes.

Step 4: Analyze the statement about the mean

The statement says: "The mean is the average of all the data values."
This is true. The mean is calculated by summing all the data values and dividing by the number of values. Mathematically, it is represented as: \[ \text{Mean} = \frac{\sum_{i=1}^{n} x_i}{n} \] where \( x_i \) are the data values and \( n \) is the number of values.

Final Answer

The true statements are:

  1. The mode is the number (or numbers) that occurs most frequently in the set.
  2. The median is the number in the middle of a set of numbers arranged in numerical order.
  3. The mean is the average of all the data values.

Thus, the final answer is:
\(\boxed{\text{True statements: 1, 2, and 4}}\)

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