Find the mean of the distribution. 130, 90, 25, 77, 250, 100

Options

A. 25
B. 77
C. 100
D. 112

Answer

To find the mean of the given distribution, we will follow these steps:

### Step 1: List the Observations
The observations given are:
- 130
- 90
- 25
- 77
- 250
- 100

### Step 2: Calculate the Sum of the Observations
We need to add all the observations together.

\[ \text{Sum} = 130 + 90 + 25 + 77 + 250 + 100 \]

Calculating this step-by-step:
- First, add 130 and 90:
\[ 130 + 90 = 220 \]
- Next, add 25:
\[ 220 + 25 = 245 \]
- Then, add 77:
\[ 245 + 77 = 322 \]
- Now, add 250:
\[ 322 + 250 = 572 \]
- Finally, add 100:
\[ 572 + 100 = 672 \]

So, the total sum of the observations is 672.

### Step 3: Count the Number of Observations
The number of observations is 6 (as there are six numbers in the list).

### Step 4: Calculate the Mean
Now, we will use the formula for the mean:

\[ \text{Mean} = \frac{\text{Sum of Observations}}{\text{Number of Observations}} = \frac{672}{6} \]

Calculating this:
- Divide 672 by 6:
\[ 672 \div 6 = 112 \]

### Conclusion
The mean of the distribution is **112**.

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