The weights (in kilogram) of 5 persons are 67, 65, 71, 57 and 45. Find the arithmetic mean of their weights.

Answer

To find the arithmetic mean of the weights of the 5 persons, we will follow these steps:

### Step 1: List the weights
The weights of the 5 persons are:
- 67 kg
- 65 kg
- 71 kg
- 57 kg
- 45 kg

### Step 2: Calculate the sum of the weights
Now, we will add all the weights together:
\[ 67 + 65 + 71 + 57 + 45 \]

Calculating this step-by-step:
- First, add 67 and 65:
\[ 67 + 65 = 132 \]
- Next, add 71:
\[ 132 + 71 = 203 \]
- Then, add 57:
\[ 203 + 57 = 260 \]
- Finally, add 45:
\[ 260 + 45 = 305 \]

So, the total sum of the weights is **305 kg**.

### Step 3: Count the number of observations
The number of persons (observations) is 5.

### Step 4: Calculate the arithmetic mean
Now we will use the formula for arithmetic mean:
\[ \text{Mean} = \frac{\text{Sum of all observations}}{\text{Total number of observations}} \]
Substituting the values we found:
\[ \text{Mean} = \frac{305}{5} \]

### Step 5: Perform the division
Now, we divide 305 by 5:
- 5 goes into 30 six times (5 x 6 = 30), leaving a remainder of 0.
- Bring down the 5, and 5 goes into 5 one time (5 x 1 = 5).

So,
\[ 305 \div 5 = 61 \]

### Final Answer
The arithmetic mean of their weights is **61 kg**.

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