Find the median of 17, 26, 60, 45, 33, 32, 29, 34 and 56. If 26 is replaced by 62, what will be the new median?

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: 17, 26, 60, 45, 33, 32, 29, 34, and 56.

Arranging them in ascending order, we get:
17, 26, 29, 32, 33, 34, 45, 56, 60

### Step 2: Count the number of observations
Now, we count the number of observations in the arranged list. The numbers are:
1. 17
2. 26
3. 29
4. 32
5. 33
6. 34
7. 45
8. 56
9. 60

There are a total of 9 observations.

### Step 3: Find the median
Since the number of observations (9) is odd, the median is the middlemost observation. The middle position can be found using the formula:
\[ \text{Median Position} = \frac{n + 1}{2} \]
where \( n \) is the number of observations.

Here, \( n = 9 \):
\[ \text{Median Position} = \frac{9 + 1}{2} = 5 \]

Thus, the median is the 5th observation in the ordered list:
1. 17
2. 26
3. 29
4. 32
5. **33** (Median)
6. 34
7. 45
8. 56
9. 60

So, the median is **33**.

### Step 4: Replace 26 with 62 and find the new median
Now, we replace 26 with 62 in the original list. The new numbers are:
17, 62, 60, 45, 33, 32, 29, 34, and 56.

### Step 5: Arrange the new numbers in ascending order
Arranging these new numbers in ascending order, we get:
17, 29, 32, 33, 34, 45, 56, 60, 62

### Step 6: Count the number of observations again
Counting the observations again, we still have:
1. 17
2. 29
3. 32
4. 33
5. 34
6. 45
7. 56
8. 60
9. 62

There are still 9 observations.

### Step 7: Find the new median
Again, since the number of observations is odd (9), we find the median using the same position:
\[ \text{Median Position} = \frac{9 + 1}{2} = 5 \]

Thus, the new median is the 5th observation in the ordered list:
1. 17
2. 29
3. 32
4. 33
5. **34** (New Median)
6. 45
7. 56
8. 60
9. 62

So, the new median is **34**.

### Summary:
- The original median is **33**.
- The new median after replacing 26 with 62 is **34**.