The median of 111, 129, 143, 118, 120, 125, 170, 162 is

Options

A. 127
B. 118
C. 111
D. 135

Answer

To find the median of the given data set: 111, 129, 143, 118, 120, 125, 170, 162, we will follow these steps:

### Step 1: Arrange the data in ascending order.
First, we need to sort the numbers from smallest to largest.

**Sorted Data:**
111, 118, 120, 125, 129, 143, 162, 170

### Step 2: Determine the number of observations (n).
Count the total number of data points.

**Total observations (n):**
n = 8 (since there are 8 numbers in the data set)

### Step 3: Identify if n is even or odd.
Since n = 8, which is even, we will use the formula for finding the median when n is even.

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

Here, n/2 = 8/2 = 4, so we will find the 4th and 5th terms in the sorted data.

### Step 5: Find the 4th and 5th terms.
From our sorted data:
- 4th term = 125
- 5th term = 129

### Step 6: Calculate the median.
Now, substitute the values into the median formula:
\[ \text{Median} = \frac{125 + 129}{2} = \frac{254}{2} = 127 \]

### Final Answer:
The median of the given data set is **127**.

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