The correct answer is:

The mean, median, and mode of the new data set are increased by 3.

Here's the reasoning:

When all data values in a data set are increased by a constant amount (in this case, 3), each of the measures of central tendency—mean, median, and mode—also increases by that same constant amount.

1. Mean: The mean is the average of all data points. If each data point increases by 3, then the total sum of the data values increases by $10 \times 3 = 30$. Dividing by the number of data points (10) shows the mean has increased by 3.

2. Median: The median is the middle value in an ordered list. Increasing each data value by 3 shifts the entire list uniformly, so the median also increases by 3.

3. Mode: The mode is the most frequently occurring value(s) in the dataset. If each value is increased by 3, the mode also increases by 3.

Thus, when each data point is uniformly increased, all measures of central tendency (mean, median, and mode) are increased by that same constant.

Would you like further details or have any questions?

Here are five related questions:

1. How does adding a constant affect the variance of a dataset?
2. If a constant is subtracted from each data point, how are the mean, median, and mode affected?
3. What happens to the mean, median, and mode if each data value is multiplied by a constant instead?
4. How do transformations affect the standard deviation of a dataset?
5. Why does adding a constant not affect the shape of a distribution?

Tip: Uniform changes to data (like adding or subtracting a constant) shift the dataset's location but do not change the spread of values.