Find the lower quartile, upper quartile and inter quartile range for the date: 9,11,15,19,17,13,7

Answer

To find the lower quartile, upper quartile, and interquartile range for the data set: 9, 11, 15, 19, 17, 13, and 7, follow these steps:

### Step 1: Arrange the Data in Ascending Order
First, we need to arrange the given data in ascending order.

**Data:** 9, 11, 15, 19, 17, 13, 7

**Ascending Order:** 7, 9, 11, 13, 15, 17, 19

### Step 2: Determine the Number of Data Points
Count the number of data points (n).

**n = 7** (There are 7 data points)

### Step 3: Calculate the Lower Quartile (Q1)
The lower quartile (Q1) is the median of the lower half of the data set.

To find Q1, we can use the formula:
\[ Q1 = \frac{n + 1}{4} \]
Substituting the value of n:
\[ Q1 = \frac{7 + 1}{4} = \frac{8}{4} = 2 \]

The second value in the ordered data is:
**Q1 = 9**

### Step 4: Calculate the Upper Quartile (Q3)
The upper quartile (Q3) is the median of the upper half of the data set.

To find Q3, we can use the formula:
\[ Q3 = \frac{3(n + 1)}{4} \]
Substituting the value of n:
\[ Q3 = \frac{3(7 + 1)}{4} = \frac{3 \times 8}{4} = 6 \]

The sixth value in the ordered data is:
**Q3 = 17**

### Step 5: Calculate the Interquartile Range (IQR)
The interquartile range (IQR) is the difference between the upper quartile and the lower quartile.

\[ IQR = Q3 - Q1 \]
Substituting the values:
\[ IQR = 17 - 9 = 8 \]

### Final Results
- Lower Quartile (Q1) = 9
- Upper Quartile (Q3) = 17
- Interquartile Range (IQR) = 8

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