Find the median and mode respectively of the given data. 24, 17, 24, 26, 13, 18, 25, 19, 16, 20, 28

Options

A. 20,24
B. 20,20
C. 18,24
D. 16,25

Answer

To find the median and mode of the given data set: 24, 17, 24, 26, 13, 18, 25, 19, 16, 20, 28, we will follow these steps:

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

**Data in ascending order:**
13, 16, 17, 18, 19, 20, 24, 24, 25, 26, 28

### Step 2: Find the median.
The median is the middle value of a data set. To find the median, we need to determine the number of data points.

**Count the number of data points:**
There are 11 data points in total (which is an odd number).

To find the median:
- The median position can be calculated using the formula: (n + 1) / 2, where n is the number of data points.
- Here, n = 11, so the median position is (11 + 1) / 2 = 12 / 2 = 6.

Now, we find the 6th value in the sorted list:
1. 13
2. 16
3. 17
4. 18
5. 19
6. **20** (This is the median)

**Median = 20**

### Step 3: Find the mode.
The mode is the value that appears most frequently in the data set.

**Count the frequency of each number:**
- 13: 1 time
- 16: 1 time
- 17: 1 time
- 18: 1 time
- 19: 1 time
- 20: 1 time
- 24: 2 times
- 25: 1 time
- 26: 1 time
- 28: 1 time

The number that appears most frequently is 24, which appears 2 times.

**Mode = 24**

### Final Answer:
**Median = 20, Mode = 24**

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