Find the median and the mode for the set of numbers : 2,2,3,5,5,5,6,8 and 9.

Answer

To find the median and mode for the set of numbers: 2, 2, 3, 5, 5, 5, 6, 8, and 9, we can follow these steps:

### Step 1: Arrange the numbers in ascending order
The given set of numbers is already arranged in ascending order:
2, 2, 3, 5, 5, 5, 6, 8, 9

### Step 2: Determine the number of observations (n)
Count the total number of observations in the set:
- Here, n = 9 (there are 9 numbers in total).

### Step 3: Find the median
Since n is odd, we can use the formula for the median:
\[ \text{Median} = \frac{n + 1}{2} \text{th term} \]
Substituting the value of n:
\[ \text{Median} = \frac{9 + 1}{2} = \frac{10}{2} = 5 \text{th term} \]

Now, we find the 5th term in the ordered list:
1st term: 2
2nd term: 2
3rd term: 3
4th term: 5
5th term: 5

Thus, the median is:
**Median = 5**

### Step 4: Find the mode
The mode is the number that occurs most frequently in the set.
Looking at the numbers:
- 2 occurs 2 times
- 3 occurs 1 time
- 5 occurs 3 times
- 6 occurs 1 time
- 8 occurs 1 time
- 9 occurs 1 time

The number that occurs the most is 5, which appears 3 times.

Thus, the mode is:
**Mode = 5**

### Final Answer:
- Median = 5
- Mode = 5

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