Find the Q1 and Q2 for the follwing distrbution . 2,4,3,7,8,9,1,14,18,16,19.

Answer

To find the first quartile (Q1) and the second quartile (Q2) for the given distribution of data, we will follow these steps:

### Step 1: Arrange the data in increasing order
The given data is: 2, 4, 3, 7, 8, 9, 1, 14, 18, 16, 19.

When we arrange this data in increasing order, we get:
1, 2, 3, 4, 7, 8, 9, 14, 16, 18, 19.

### Step 2: Count the number of data points (N)
Now, we count the number of data points in the arranged list:
N = 11 (there are 11 data points).

### Step 3: Calculate Q1
Q1 represents the 25th percentile. To find Q1, we use the formula:
\[ Q1 = \frac{N + 1}{4} \]

Substituting N = 11 into the formula:
\[ Q1 = \frac{11 + 1}{4} = \frac{12}{4} = 3 \]

This means Q1 is the value at the 3rd position in the ordered list. Looking at our ordered list:
1 (1st), 2 (2nd), 3 (3rd).

Thus, Q1 = 3.

### Step 4: Calculate Q2
Q2 represents the median (50th percentile). To find Q2, we use the formula:
\[ Q2 = \frac{N + 1}{2} \]

Substituting N = 11 into the formula:
\[ Q2 = \frac{11 + 1}{2} = \frac{12}{2} = 6 \]

This means Q2 is the value at the 6th position in the ordered list. Looking at our ordered list:
1 (1st), 2 (2nd), 3 (3rd), 4 (4th), 7 (5th), 8 (6th).

Thus, Q2 = 8.

### Final Results
- Q1 = 3
- Q2 = 8