The ages of 15 students in years) in a summer camp are as follows: 11, 14, 13, 15, 16, 10, 12, 12, 14, 11, 10, 12, 13, 15, 11 Find: The mean age.

Answer

To find the mean age of the 15 students in the summer camp, we will follow these steps:

### Step 1: List the ages
The ages of the 15 students are:
11, 14, 13, 15, 16, 10, 12, 12, 14, 11, 10, 12, 13, 15, 11

### Step 2: Sum the ages
Now, we will add all the ages together:
\[ 11 + 14 + 13 + 15 + 16 + 10 + 12 + 12 + 14 + 11 + 10 + 12 + 13 + 15 + 11 \]

Calculating this step-by-step:
- \( 11 + 14 = 25 \)
- \( 25 + 13 = 38 \)
- \( 38 + 15 = 53 \)
- \( 53 + 16 = 69 \)
- \( 69 + 10 = 79 \)
- \( 79 + 12 = 91 \)
- \( 91 + 12 = 103 \)
- \( 103 + 14 = 117 \)
- \( 117 + 11 = 128 \)
- \( 128 + 10 = 138 \)
- \( 138 + 12 = 150 \)
- \( 150 + 13 = 163 \)
- \( 163 + 15 = 178 \)
- \( 178 + 11 = 189 \)

So, the total sum of the ages is \( 189 \).

### Step 3: Count the number of observations
The number of students (observations) is given as 15.

### Step 4: Calculate the mean
The mean is calculated by dividing the sum of the ages by the number of observations:
\[ \text{Mean} = \frac{\text{Sum of ages}}{\text{Number of observations}} = \frac{189}{15} \]

### Step 5: Perform the division
Now, we divide \( 189 \) by \( 15 \):
- \( 15 \) goes into \( 189 \) a total of \( 12 \) times (since \( 15 \times 12 = 180 \)).
- Subtract \( 180 \) from \( 189 \) to get a remainder of \( 9 \).
- Now, we add a decimal point and a zero to the remainder, making it \( 90 \).
- \( 15 \) goes into \( 90 \) a total of \( 6 \) times (since \( 15 \times 6 = 90 \)).
- There is no remainder left.

Thus, we find:
\[ \text{Mean} = 12.6 \]

### Final Answer
The mean age of the students is \( 12.6 \) years.

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