Directions for questions : State whether the following statements are true or false.
The mean of the observations 9, 7, 11, 13, 2, 4, 5, 5 is 7.

Answer

To determine whether the statement "The mean of the observations 9, 7, 11, 13, 2, 4, 5, 5 is 7" is true or false, we will calculate the mean step by step.

### Step 1: List the Observations
The given observations are:
- 9
- 7
- 11
- 13
- 2
- 4
- 5
- 5

### Step 2: Count the Number of Observations
We count how many observations there are:
- Total observations = 8

### Step 3: Calculate the Sum of the Observations
Now, we need to add all the observations together:
\[ 9 + 7 + 11 + 13 + 2 + 4 + 5 + 5 \]
Calculating this step by step:
- \(9 + 7 = 16\)
- \(16 + 11 = 27\)
- \(27 + 13 = 40\)
- \(40 + 2 = 42\)
- \(42 + 4 = 46\)
- \(46 + 5 = 51\)
- \(51 + 5 = 56\)

So, the sum of the observations is 56.

### Step 4: Calculate the Mean
The mean is calculated using the formula:
\[ \text{Mean} = \frac{\text{Sum of Observations}}{\text{Total Number of Observations}} \]
Substituting the values we found:
\[ \text{Mean} = \frac{56}{8} \]
Calculating this gives:
\[ \text{Mean} = 7 \]

### Step 5: Compare the Calculated Mean with the Given Statement
The calculated mean is 7, which matches the statement in the question.

### Conclusion
Therefore, the statement "The mean of the observations 9, 7, 11, 13, 2, 4, 5, 5 is 7" is **True**.

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