Find the mean of t + 2, 2t - 4, 3t + 2 and 2t.

Analysis

To find the mean (average) of a set of values, you must sum all the individual terms and then divide that sum by the total number of terms provided.

Concept

The formula for the mean ($\bar{x}$) is:

Where:

• $\sum x$ is the sum of all the terms.
• $n$ is the number of terms.

Step-by-Step Solution

Step 1: Identify the terms and the count ($n$). The terms are: $(t + 2)$, $(2t - 4)$, $(3t + 2)$, and $(2t)$. There are $n = 4$ terms.

Step 2: Calculate the sum of the terms. Sum $= (t + 2) + (2t - 4) + (3t + 2) + (2t)$

Group the like terms (the $t$ terms together and the constants together): Sum $= (t + 2t + 3t + 2t) + (2 - 4 + 2)$ Sum $= (8t) + (0)$ Sum $= 8t$

Step 3: Divide the sum by the number of terms ($n$). Mean $= \frac{8t}{4}$ Mean $= 2t$

Conclusion

Comparing our result to the given options, $2t$ corresponds to option B.

Exam Tip

When dealing with algebraic expressions in statistics, always be careful with the signs (positive and negative) when grouping terms. In this case, $(2 - 4 + 2)$ equals zero, which simplified the expression significantly. Always check your arithmetic at this stage to avoid silly mistakes!