`Q_(2)` for the data: 13, 16, 28, 17, 12, 25, 26, 19, 27, 21 is :

Options

A. 21
B. 19
C. 20
D. 25

Answer

To find the second quartile (Q2) for the given data set, we will follow these steps:

### Step 1: Arrange the data in ascending order.
The given data is: 13, 16, 28, 17, 12, 25, 26, 19, 27, 21.

When we arrange this data in ascending order, we get:
12, 13, 16, 17, 19, 21, 25, 26, 27, 28.

### Step 2: Determine the number of observations (n).
Count the number of data points in the arranged data:
- There are 10 observations (n = 10).

### Step 3: Identify the position of Q2 (median).
Since Q2 is the median, we need to find the middle value(s) of the data. For an even number of observations, the median is calculated as the average of the two middle numbers.

To find the position of Q2:
- For n = 10 (even), the median position is given by:
\[ \text{Median position} = \frac{n}{2} = \frac{10}{2} = 5 \]
and the next position is:
\[ \text{Next position} = \frac{n}{2} + 1 = 5 + 1 = 6 \]

### Step 4: Find the values at the 5th and 6th positions.
From our arranged data:
- The 5th term is 19.
- The 6th term is 21.

### Step 5: Calculate Q2 (median).
Now, we take the average of the 5th and 6th terms:
\[ Q2 = \frac{\text{5th term} + \text{6th term}}{2} = \frac{19 + 21}{2} = \frac{40}{2} = 20. \]

Thus, the second quartile (Q2) for the given data is **20**.

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