Find the average of 205, 302, 108, 403 and 202

### Concept & Formula The arithmetic mean (average) is calculated by adding all the numbers in the dataset and dividing by the total count of numbers. $$Average = \frac{\text{Sum of all observations}}{\text{Total number of observations}}$$ ### Step-by-Step Solution * **Calculation:** Add the five given numbers together. Sum = $205 + 302 + 108 + 403 + 202$ Sum = $1220$ * **Calculation:** Count the number of observations. There are 5 numbers. * **Calculation:** Divide the sum by the count. Average = $\frac{1220}{5}$ Average = $244$ ### Exam Strategy & Shortcut **Assumed Mean Method:** Pick a convenient number close to the values, say 200. Let's find the deviations from 200: 205 $\rightarrow +5$ 302 $\rightarrow +102$ 108 $\rightarrow -92$ 403 $\rightarrow +203$ 202 $\rightarrow +2$ Sum of deviations = $5 + 102 - 92 + 203 + 2 = 220$. Average of deviations = $\frac{220}{5} = 44$. Final Average = Assumed Mean + Average of deviations = $200 + 44 = 244$. This method prevents dealing with large sums and reduces arithmetic errors. ### Common Pitfall A common trap in multiple-choice questions is presenting the "Sum" as one of the options. Notice that 1220 is option (d). Students who calculate the sum but forget to divide by $N$ will prematurely select (d) and lose marks. Always complete the final division step. ### Final Answer **Therefore, the correct answer is 244.**