Find the median of 241,243,347,350,327,299,261,292,271,258 and 257

Answer

To find the median of the given data set: 241, 243, 347, 350, 327, 299, 261, 292, 271, 258, and 257, we will follow these steps:

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

The given numbers are:
241, 243, 347, 350, 327, 299, 261, 292, 271, 258, and 257.

Arranging them in ascending order, we get:
241, 243, 257, 258, 261, 271, 292, 299, 327, 347, 350.

### Step 2: Count the number of observations.
Next, we need to determine how many numbers are in our data set.

Counting the numbers, we find there are 11 observations.

### Step 3: Determine if the number of observations is odd or even.
Since we have 11 observations, which is an odd number, we will use the formula for finding the median in a data set with an odd number of observations.

### Step 4: Use the median formula.
The formula for finding the median when the number of observations (n) is odd is:
\[ \text{Median} = \frac{n + 1}{2} \text{th term} \]
Here, \( n = 11 \).

Calculating:
\[ \text{Median} = \frac{11 + 1}{2} = \frac{12}{2} = 6 \]
So, the median is the 6th term in our ordered list.

### Step 5: Identify the 6th term.
Now, we will locate the 6th term in our ordered list:
1. 241
2. 243
3. 257
4. 258
5. 261
6. **271** (This is the 6th term)
7. 292
8. 299
9. 327
10. 347
11. 350

### Final Answer:
The median of the given data set is **271**.

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