The marks of six boys in a group are 48, 59, 87, 37, 78 and 57. What are the average marks of all six boys?

### Concept & Formula This is a fundamental average problem. The arithmetic mean (average) is calculated by taking the sum of all the individual values in a dataset and dividing it by the total count of those values. $$\text{Average} = \frac{\text{Sum of all observations}}{\text{Total number of observations}}$$ ### Step-by-Step Solution * **Step 1: Calculate the Sum** We need to add all six given marks together. $$\text{Sum} = 48 + 59 + 87 + 37 + 78 + 57$$ Let's group them for easier addition: $(48 + 59) = 107$ $(87 + 37) = 124$ $(78 + 57) = 135$ Total Sum = $107 + 124 + 135 = 366$ * **Step 2: Identify the Count** The problem states there are six boys. Therefore, the total number of observations is 6. * **Step 3: Calculate the Average** $$\text{Average} = \frac{366}{6}$$ $$\text{Average} = 61$$ ### Exam Strategy & Shortcut **Unit Digit Check:** To save time on long division, first calculate just the unit digit of the sum. $8 + 9 + 7 + 7 + 8 + 7 = 46$ $\rightarrow$ The sum ends in a 6. We need to divide a number ending in 6 by 6. Looking at the options: (a) $61 \times 6 = 366$ (Ends in 6 - Possible) (b) $65 \times 6 = 390$ (Ends in 0 - Incorrect) (c) $69 \times 6 = 414$ (Ends in 4 - Incorrect) Since only option (a) provides a valid unit digit when multiplied back by 6, you can confidently mark 61 without doing the full addition and division, provided you trust the options don't hide behind "None of these". ### Common Pitfall A common mistake in simple addition problems under time pressure is misaligning columns or carrying over the wrong digit. Grouping the numbers into pairs (as shown in Step 1) or using the unit digit shortcut helps minimize arithmetic fatigue. ### Final Answer **Therefore, the correct answer is 61.**