The body weight of seven students of a class is recorded as $54$ kg, $78$ kg, $43$ kg, $82$ kg, $67$ kg, $42$ kg and $75$ kg. What is the average body weight of all the seven students?

### Concept & Formula The average (or arithmetic mean) of a set of values is calculated by adding all the values together and dividing by the total number of values. $$ \text{Average} = \frac{\text{Sum of all observations}}{\text{Number of observations}} $$ ### Step-by-Step Solution * **Given:** The weights are $54$, $78$, $43$, $82$, $67$, $42$, and $75$ kg. The total number of students ($N$) is $7$. * **Calculation:** First, find the total sum of the weights: $\text{Sum} = 54 + 78 + 43 + 82 + 67 + 42 + 75 = 441$ kg Next, divide the sum by the number of students: $\text{Average} = \frac{441}{7}$ $\text{Average} = 63$ kg ### Exam Strategy & Shortcut **Deviation Method:** Choose a convenient assumed mean, like $60$. Find the deviations of each weight from $60$: $-6$, $+18$, $-17$, $+22$, $+7$, $-18$, $+15$. Notice $+18$ and $-18$ cancel out perfectly. Sum of remaining deviations = $-6 - 17 + 22 + 7 + 15 = 21$. Average deviation = $\frac{21}{7} = +3$. Actual Average = Assumed Mean + Average Deviation = $60 + 3 = 63$. This completely avoids adding large numbers and saves valuable seconds! ### Common Pitfall Students often make basic addition errors when summing a long list of two-digit numbers under time pressure. Grouping numbers that form multiples of $10$ (e.g., $78 + 42 = 120$) can help prevent these careless arithmetic mistakes. ### Final Answer **Therefore, the correct answer is 63 kg.**