Find the `Q_(2)` for the following distribution. 30, 42, 33, 31, 40, 45, 34, 47, 39

Answer

To find the second quartile (Q2) for the given distribution of numbers, we can follow these steps:

### Step 1: Arrange the data in ascending order
We start by arranging the given numbers in increasing order.

**Given numbers:** 30, 42, 33, 31, 40, 45, 34, 47, 39

**Arranged in ascending order:** 30, 31, 33, 34, 39, 40, 42, 45, 47

### Step 2: Determine the number of observations
Count the number of observations (n). In this case, we have 9 observations.

**n = 9**

### Step 3: Find the position of Q2 (Median)
The second quartile (Q2) is the median of the data set. The median can be found using the formula:

\[ \text{Median position} = \frac{n + 1}{2} \]

Substituting the value of n:

\[ \text{Median position} = \frac{9 + 1}{2} = \frac{10}{2} = 5 \]

### Step 4: Identify the median value
Now, we look for the value at the 5th position in the arranged data.

**Arranged data:** 30, 31, 33, 34, **39**, 40, 42, 45, 47

The 5th term is **39**.

### Conclusion
Thus, the second quartile (Q2) for the given distribution is **39**.

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