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, we will follow these steps:

### Step 1: Arrange the data in ascending order
The given data is:
24, 17, 24, 26, 13, 18, 25, 19, 16, 20, 28

Arranging this data in ascending order gives us:
13, 16, 17, 18, 19, 20, 24, 24, 24, 25, 26, 28

### Step 2: Find the median
To find the median, we first determine the number of data points (n).

Counting the arranged data:
1. 13
2. 16
3. 17
4. 18
5. 19
6. 20
7. 24
8. 24
9. 24
10. 25
11. 26
12. 28

There are 11 data points (n = 11), which is odd.

The formula for the median in an odd set is:
\[ \text{Median} = \text{Value at position} \left( \frac{n + 1}{2} \right) \]

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

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

Thus, the median is **20**.

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

From the arranged data:
- 13 appears 1 time
- 16 appears 1 time
- 17 appears 1 time
- 18 appears 1 time
- 19 appears 1 time
- 20 appears 1 time
- 24 appears 3 times
- 25 appears 1 time
- 26 appears 1 time
- 28 appears 1 time

The number that appears most frequently is **24**, which appears 3 times.

Thus, the mode is **24**.

### Final Answer
The median is **20** and the mode is **24**.

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