If the strengths of 10 classes in a school are given as 28, 42, 25, 30, 45, 22, 25, 34, 26 and 36, then find the median strength.

Answer

To find the median strength of the classes, follow these steps:

### Step 1: Arrange the data in ascending order
The strengths of the classes are given as:
28, 42, 25, 30, 45, 22, 25, 34, 26, and 36.

First, we need to arrange these numbers in ascending order:
- The smallest number is 22.
- Next, we have 25 (which appears three times).
- Then we have 26, 28, 30, 34, 36, 42, and finally 45.

So, the arranged data is:
22, 25, 25, 25, 26, 28, 30, 34, 36, 42, 45.

### Step 2: Determine the number of observations (n)
Count the number of observations in the arranged data.
In this case, n = 10 (since there are 10 classes).

### Step 3: Find the median
Since the number of observations (n) is even, the median is calculated using the formula:
\[ \text{Median} = \frac{\text{(n/2)th observation} + \text{(n/2 + 1)th observation}}{2} \]

Here, n = 10, so:
- n/2 = 10/2 = 5
- n/2 + 1 = 5 + 1 = 6

Now, we need to find the 5th and 6th observations in the arranged data:
- The 5th observation is 26.
- The 6th observation is 28.

Now, substitute these values into the median formula:
\[ \text{Median} = \frac{26 + 28}{2} = \frac{54}{2} = 27 \]

### Final Answer
The median strength of the classes is **27**.

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