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Understanding the mode is quite simple. It represents the most frequently occurring number in a set of data. For example, in the dataset \(2, 2, 3, 6, 10\), the number 2 appears more frequently than the others, making 2 the mode. Knowing the mode can be particularly useful when you want to identify which item or value appears the most in a dataset.

When you add a constant to each value in the dataset, such as adding 5 to each number in the original dataset to get \(7, 7, 8, 11, 15\), the mode shifts by the same constant. Originally, the mode was 2; after adding 5 to every value in the dataset, the new mode becomes 7. This shows that the mode changes according to the constant added, maintaining the same frequency pattern as before.

• Key takeaway: Adding or subtracting a fixed number to all elements in a dataset will change the mode by this constant if the mode repeats with the same frequency.

To find the median, you need to organize your dataset in increasing order and select the middle value. If there's an odd number of data points, it's simple—you pick the middle one. In our dataset \(2, 2, 3, 6, 10\), after arranging these values (which are already in order), the third number is 3. This is your median.

Adding a constant shifts all numbers evenly, so when you add 5 to each number, making the dataset \(7, 7, 8, 11, 15\), the median becomes 8. Every element shifts, including the median, by the same constant, preserving the distinct middle position.

• Key takeaway: Adding or subtracting a fixed number from every point in a data set will translate the median by this constant without affecting the order.

The mean, or average, is calculated as the sum of all values divided by the number of values. For our initial set \(2, 2, 3, 6, 10\), you calculate it by adding the numbers (23) and dividing by the total quantity (5), resulting in a mean of 4.6.

When a constant is added to each number in your dataset, such as 5 in our example, the overall sum increases proportionally for each added constant. So, the mean moves from 4.6 to 9.6 when 5 is added to each number, reinforcing the idea that every number in the dataset has been altered equally.

• Key takeaway: The mean reflects even distribution across a dataset. Adding a constant to each number will result in an equivalent shift in the mean by that constant.