The ages (in years) of 10 teachers in a school are
34, 37, 53, 46, 52, 43, 31, 36, 40, 50
Find the median age

Answer

To find the median age of the 10 teachers, we will follow these steps:

### Step 1: Organize the Data
First, we need to arrange the ages of the teachers in ascending order. The ages given are:
34, 37, 53, 46, 52, 43, 31, 36, 40, 50

When we arrange them in ascending order, we get:
31, 34, 36, 37, 40, 43, 46, 50, 52, 53

### Step 2: Identify the Number of Terms
Next, we identify the number of terms (n) in the data. In this case, there are 10 teachers, so:
n = 10

### Step 3: Apply the Median Formula for Even Numbers
Since we have an even number of terms (10), we use the formula for median:
\[ \text{Median} = \frac{\text{n/2 th term} + \text{(n/2 + 1) th term}}{2} \]
Here, n/2 = 10/2 = 5, so we will find the 5th and 6th terms.

### Step 4: Find the 5th and 6th Terms
From our ordered list:
1. 31 (1st term)
2. 34 (2nd term)
3. 36 (3rd term)
4. 37 (4th term)
5. 40 (5th term)
6. 43 (6th term)

Thus, the 5th term is 40 and the 6th term is 43.

### Step 5: Calculate the Median
Now, we substitute the values into the median formula:
\[ \text{Median} = \frac{40 + 43}{2} = \frac{83}{2} = 41.5 \]

### Final Answer
The median age of the teachers is **41.5 years**.

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