Average weight of 19 men is 74kg and the average weight of 38 women is 63kg.What is the average weight (rounded off to the nearnest integer) of all the men and the women together?

Options

A. 59 kg
B. 65kg
C. 69 kg
D. 71 kg

Answer

To find the average weight of all the men and women together, we will follow these steps:

### Step 1: Calculate the total weight of the men.
The average weight of the men is given as 74 kg, and there are 19 men.

\[ \text{Total weight of men} = \text{Average weight of men} \times \text{Number of men} \]
\[ \text{Total weight of men} = 74 \, \text{kg} \times 19 = 1406 \, \text{kg} \]

### Step 2: Calculate the total weight of the women.
The average weight of the women is given as 63 kg, and there are 38 women.

\[ \text{Total weight of women} = \text{Average weight of women} \times \text{Number of women} \]
\[ \text{Total weight of women} = 63 \, \text{kg} \times 38 = 2394 \, \text{kg} \]

### Step 3: Calculate the total weight of all individuals (men and women).
Now, we add the total weight of men and women together.

\[ \text{Total weight} = \text{Total weight of men} + \text{Total weight of women} \]
\[ \text{Total weight} = 1406 \, \text{kg} + 2394 \, \text{kg} = 3800 \, \text{kg} \]

### Step 4: Calculate the total number of individuals.
Now, we find the total number of individuals by adding the number of men and women.

\[ \text{Total number of individuals} = \text{Number of men} + \text{Number of women} \]
\[ \text{Total number of individuals} = 19 + 38 = 57 \]

### Step 5: Calculate the average weight of all individuals.
Finally, we can find the average weight by dividing the total weight by the total number of individuals.

\[ \text{Average weight} = \frac{\text{Total weight}}{\text{Total number of individuals}} \]
\[ \text{Average weight} = \frac{3800 \, \text{kg}}{57} \approx 66.67 \, \text{kg} \]

### Step 6: Round off the average weight.
Rounding off 66.67 to the nearest integer gives us:

\[ \text{Average weight (rounded)} = 67 \, \text{kg} \]

### Final Answer:
The average weight of all the men and women together is **67 kg**.

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