The median of the numbers 45, 34, 65, 48, 93, 54, 22, 86, 45, 87 is

Options

A. 51
B. 49.5
C. 54
D. 56

Answer

To find the median of the given numbers, we will follow these steps:

### Step 1: Arrange the numbers in ascending order.
The given numbers are: 45, 34, 65, 48, 93, 54, 22, 86, 45, 87.

**Arranging them in ascending order:**
22, 34, 45, 45, 48, 54, 65, 86, 87, 93

### Step 2: Count the total number of observations (n).
In this case, we have 10 numbers.

**Total observations (n) = 10**

### Step 3: Determine if n is even or odd.
Since n = 10, which is an even number, we will use the formula for finding the median for an even set of numbers.

### Step 4: Use the median formula for even n.
The formula for the median when n is even is:
\[ \text{Median} = \frac{\text{n/2-th observation} + \text{(n/2 + 1)-th observation}}{2} \]

### Step 5: Calculate n/2.
\[ n/2 = 10/2 = 5 \]
This means we will find the 5th and 6th observations.

### Step 6: Identify the 5th and 6th observations from the ordered list.
From our ordered list:
- 5th observation = 48
- 6th observation = 54

### Step 7: Calculate the median.
Now, we can substitute these values into the median formula:
\[ \text{Median} = \frac{48 + 54}{2} \]
\[ \text{Median} = \frac{102}{2} = 51 \]

### Final Answer:
The median of the given numbers is **51**.

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