Find the mode and median of 3,4,5,5,3,6,7,3,5,5,6.

Options

A. 5 and 5
B. 3 and 5
C. 5 and 4
D. 3 and 4

Answer

To find the mode and median of the given numbers: 3, 4, 5, 5, 3, 6, 7, 3, 5, 5, 6, we will follow these steps:

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

**Sorted List:** 3, 3, 3, 4, 5, 5, 5, 5, 6, 6, 7

### Step 2: Find the mode.
The mode is the number that appears most frequently in the data set.

- Count the occurrences:
- 3 appears 3 times
- 4 appears 1 time
- 5 appears 4 times
- 6 appears 2 times
- 7 appears 1 time

Since 5 appears the most frequently (4 times), the mode is:

**Mode:** 5

### Step 3: Find the median.
The median is the middle value when the numbers are arranged in order. If there is an odd number of observations, the median is the middle number.

- Count the total number of observations: There are 11 numbers in total.
- Since 11 is odd, the median will be the value at the (n + 1) / 2 position, where n is the number of observations.

Calculating the position:
\[ \text{Position} = \frac{11 + 1}{2} = \frac{12}{2} = 6 \]

Now, we find the 6th term in the sorted list:
1. 3
2. 3
3. 3
4. 4
5. 5
6. **5** (This is the 6th term)

Thus, the median is:

**Median:** 5

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

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