The monthly incomes of five persons are ₹ $1132$, ₹ $1140$, ₹ $1144$, ₹ $1136$ and ₹ $1148$ respectively. What is their arithmetic mean?

### Concept & Strategy When a set of numbers forms an Arithmetic Progression (i.e., the difference between consecutive terms is constant), the average is simply the middle term (for an odd number of terms) or the average of the two middle terms (for an even number). ### Step-by-Step Solution * **Given:** The five incomes are ₹ $1132$, ₹ $1140$, ₹ $1144$, ₹ $1136$, and ₹ $1148$. * **Deduction & Calculation:** First, arrange the numbers in strictly ascending order to check for a pattern: $1132, 1136, 1140, 1144, 1148$ Notice that the difference between each consecutive term is exactly $4$. This confirms the series is an Arithmetic Progression (A.P.). Since there are $5$ terms (an odd number), the arithmetic mean is exactly the middle term. The middle term (the 3rd term in the sequence) is $1140$. ### Exam Strategy & Shortcut **Observation Method:** Do not waste time adding these five large numbers together! By quickly scanning the values, you can see they are perfectly symmetrical around $1140$. The deviations from $1140$ are $-8$, $-4$, $0$, $+4$, and $+8$. These deviations instantly cancel each other out, mathematically guaranteeing that $1140$ is the mean. ### Common Pitfall The most common pitfall here is resorting to the standard formula ($\frac{\text{Sum}}{\text{Count}}$) blindly. Adding five 4-digit numbers takes significantly longer, introduces a high risk of calculation errors, and wastes precious exam time when a conceptual shortcut exists. ### Final Answer **Therefore, the correct answer is ₹ 1140.**