Find the average of the following sets of scores: $385$, $441$, $876$, $221$, $536$, $46$, $291$, $428$

### Concept & Formula The average of a discrete dataset is found by taking the total sum of all the data points and dividing it by the total count of the data points. $$ \text{Average} = \frac{\text{Sum of scores}}{\text{Total number of scores}} $$ ### Step-by-Step Solution * **Given:** The scores are $385$, $441$, $876$, $221$, $536$, $46$, $291$, and $428$. By counting them, we determine there are $8$ scores in total. * **Calculation:** Add all the individual scores together to find the sum: $\text{Sum} = 385 + 441 + 876 + 221 + 536 + 46 + 291 + 428$ $\text{Sum} = 3224$ Now, divide this total sum by the number of scores ($8$): $\text{Average} = \frac{3224}{8}$ $\text{Average} = 403$ ### Exam Strategy & Shortcut **Unit Digit Verification:** When adding the numbers, check the unit digits: $5+1+6+1+6+6+1+8 = 34$. The sum ends in $4$. You are calculating $\frac{\text{Sum}}{8}$. You need a number that, when multiplied by $8$, gives a unit digit of $4$. Looking at the options, $3 \times 8 = 24$ (ends in $4$). Thus, option (b) $403$ is an extremely strong candidate, drastically reducing the need to double-check the entire arithmetic sum manually. ### Common Pitfall Skipping a number or misaligning digits during manual addition is the single biggest cause of errors here. Always write the numbers neatly in a vertical column if you choose to sum them manually, or use the unit/tens digit approximation trick to verify. ### Final Answer **Therefore, the correct answer is 403.**