What will the Arithmetic Mean of the following series ?
13, 10, 17, 15, 25

Question

What will the Arithmetic Mean of the following series ? 
13, 10, 17, 15, 25

Accepted Answer

To find the Arithmetic Mean (or average) of a series of numbers, we sum all the numbers in the series and then divide by the total count of numbers in the series.

Let's apply this to the given series: 13, 10, 17, 15, 25.

**1. Justification for Option 1 (16) being correct:**

*   **Step 1: Sum the numbers in the series.**
    Sum = 13 + 10 + 17 + 15 + 25
    Sum = 23 + 17 + 15 + 25
    Sum = 40 + 15 + 25
    Sum = 55 + 25
    Sum = 80

*   **Step 2: Count the total number of values in the series.**
    There are 5 numbers in the series (13, 10, 17, 15, 25).

*   **Step 3: Divide the sum by the count.**
    Arithmetic Mean = Sum / Count
    Arithmetic Mean = 80 / 5
    Arithmetic Mean = 16

Therefore, the Arithmetic Mean of the given series is 16, which corresponds to Option 1.

**2. Explanation for why other options are incorrect:**

*   **Option 2 (18):**
    If the arithmetic mean were 18, the sum of the numbers would have to be 18 * 5 = 90. However, the actual sum of the numbers is 80. Since 80 ≠ 90, 18 is not the correct arithmetic mean.

*   **Option 3 (20):**
    If the arithmetic mean were 20, the sum of the numbers would have to be 20 * 5 = 100. However, the actual sum of the numbers is 80. Since 80 ≠ 100, 20 is not the correct arithmetic mean.

*   **Option 4 (27):**
    If the arithmetic mean were 27, the sum of the numbers would have to be 27 * 5 = 135. However, the actual sum of the numbers is 80. Since 80 ≠ 135, 27 is not the correct arithmetic mean.

Based on the correct calculation, Option 1, which is 16, is the only correct answer for the Arithmetic Mean of the given series.