The weights of 9 boxes in kgms are as follows:
27.5, 31.2, 28.0, 32.0, 29.8, 30.3, 92.0, 28.7, 31.5
Find the appropriate average weight of the boxes.

Answer

To find the appropriate average weight of the boxes, we will calculate the mean of the given weights. The mean is calculated by summing all the observations and dividing by the total number of observations.

### Step 1: List the weights of the boxes
The weights of the boxes are:
- 27.5 kg
- 31.2 kg
- 28.0 kg
- 32.0 kg
- 29.8 kg
- 30.3 kg
- 92.0 kg
- 28.7 kg
- 31.5 kg

### Step 2: Sum all the weights
Now, we will add all the weights together:
\[ 27.5 + 31.2 + 28.0 + 32.0 + 29.8 + 30.3 + 92.0 + 28.7 + 31.5 \]

Calculating this step-by-step:
- \(27.5 + 31.2 = 58.7\)
- \(58.7 + 28.0 = 86.7\)
- \(86.7 + 32.0 = 118.7\)
- \(118.7 + 29.8 = 148.5\)
- \(148.5 + 30.3 = 178.8\)
- \(178.8 + 92.0 = 270.8\)
- \(270.8 + 28.7 = 299.5\)
- \(299.5 + 31.5 = 331.0\)

So, the total sum of the weights is \(331.0\) kg.

### Step 3: Count the total number of observations
The total number of boxes (observations) is \(9\).

### Step 4: Calculate the mean
Now, we will calculate the mean by dividing the total sum by the number of observations:
\[ \text{Mean} = \frac{\text{Total Sum}}{\text{Number of Observations}} = \frac{331.0}{9} \]

Calculating this gives:
\[ \text{Mean} = 36.7777 \ldots \approx 36.78 \text{ kg (rounded to two decimal places)} \]

### Final Answer
The appropriate average weight of the boxes is approximately **36.78 kg**.

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