Find the median of:
(i) 17,19,32,10,22,21,9,35
(ii) 72,63,29,51,35,60,55,91,85,82
(iii) 10,75,3,15,9,47,12,48,4,81,17,27

Answer

To find the median of the given sets of numbers, we will follow these steps for each part:

### Part (i): Find the median of 17, 19, 32, 10, 22, 21, 9, 35

**Step 1: Arrange the data in ascending order.**
- The numbers in ascending order are: 9, 10, 17, 19, 21, 22, 32, 35.

**Step 2: Count the number of terms.**
- There are 8 terms (which is an even number).

**Step 3: Use the median formula for even numbers.**
- The formula for the median when there are an even number of terms (N) is:
\[ \text{Median} = \frac{\text{(N/2)th term} + \text{((N/2) + 1)th term}}{2} \]
- Here, N = 8, so:
- (N/2) = 4th term
- ((N/2) + 1) = 5th term

**Step 4: Identify the 4th and 5th terms.**
- The 4th term is 19 and the 5th term is 21.

**Step 5: Calculate the median.**
\[ \text{Median} = \frac{19 + 21}{2} = \frac{40}{2} = 20 \]

### Part (ii): Find the median of 72, 63, 29, 51, 35, 60, 55, 91, 85, 82

**Step 1: Arrange the data in ascending order.**
- The numbers in ascending order are: 29, 35, 51, 55, 60, 63, 72, 82, 85, 91.

**Step 2: Count the number of terms.**
- There are 10 terms (which is an even number).

**Step 3: Use the median formula for even numbers.**
- Here, N = 10, so:
- (N/2) = 5th term
- ((N/2) + 1) = 6th term

**Step 4: Identify the 5th and 6th terms.**
- The 5th term is 60 and the 6th term is 63.

**Step 5: Calculate the median.**
\[ \text{Median} = \frac{60 + 63}{2} = \frac{123}{2} = 61.5 \]

### Part (iii): Find the median of 10, 75, 3, 15, 9, 47, 12, 48, 4, 81, 17, 27

**Step 1: Arrange the data in ascending order.**
- The numbers in ascending order are: 3, 4, 9, 10, 12, 15, 17, 27, 47, 48, 75, 81.

**Step 2: Count the number of terms.**
- There are 12 terms (which is an even number).

**Step 3: Use the median formula for even numbers.**
- Here, N = 12, so:
- (N/2) = 6th term
- ((N/2) + 1) = 7th term

**Step 4: Identify the 6th and 7th terms.**
- The 6th term is 15 and the 7th term is 17.

**Step 5: Calculate the median.**
\[ \text{Median} = \frac{15 + 17}{2} = \frac{32}{2} = 16 \]

### Summary of Medians:
- (i) Median = 20
- (ii) Median = 61.5
- (iii) Median = 16