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The mean, often referred to as the arithmetic average, serves as a measure of central tendency. It provides a useful summary of the data set by calculating what is considered a 'typical' value. To find the mean, add up all the values in the data set and then divide by the number of values. For example, for the data set \(2, 2, 3, 6, 10\), the mean is computed as:
\[\text{Mean} = \frac{2 + 2 + 3 + 6 + 10}{5} = \frac{23}{5} = 4.6\] This calculation demonstrates that the mean serves as a balance point of the data, with smaller values offset by larger ones.
When you multiply each data value by a constant, the mean also scales by that constant. If the original data set is multiplied by 5, the new mean becomes:
\[\text{New Mean} = 4.6 \times 5 = 23\]This shows that simple scaling operations affect the mean linearly, maintaining the proportionality of the data.

The median provides a measure of central tendency that identifies the middle value in an ordered data set. To find the median, sort the data in ascending order and select the middle number. If there is an odd number of values, the median is the value directly in the middle. If the data set is even, the median is the average of the two central numbers.
Consider again our data set \(2, 2, 3, 6, 10\). Ordered, the median is:
- For data: \(2, 2, 3, 6, 10\), the middle value is \(3\).
When every data point is multiplied by the same constant, the median also scales by that constant. For example, when multiplying each value by 5, the new data set becomes \(10, 10, 15, 30, 50\), with a median of:
- Median: \(15\) (as it is the new middle value).
Notice how the position, rather than the arithmetic, identifies the median. Its transformation upon multiplication strictly follows that of each data point.

The mode is the value that appears most frequently within a data set, making it a quick way to see which number is the most common. Determining the mode is simply a matter of counting how many times each number appears in the list.
In the provided data set \(2, 2, 3, 6, 10\), the number \(2\) appears twice, more frequently than the others, designating it as the mode.
When multiplying each value by a constant, the mode of the new set is also the mode of the original data but multiplied by that constant. For our exercise, the new data \(10, 10, 15, 30, 50\) yields a mode of \(10\), since:

• \(10\) appears twice.
• Original mode \(2\) × multiplier \(5\) = new mode \(10\).

The mode offers a straightforward reflection of how often a particular value occurs and scales directly with multiplicative changes to the data set.