For the data given the inter-quartile range is

Options

A. 7
B. 19
C. 14
D. 9

Answer

To find the inter-quartile range (IQR) for the given data set, we will follow these steps:

### Step 1: Arrange the Data in Ascending Order
The given data is: 7, 19, 14, and 9.

Arranging this data in ascending order, we get:
\[ 7, 9, 14, 19 \]

### Step 2: Find the Median
Since there are 4 data points (an even number), the median will be the average of the two middle numbers. The middle numbers are 9 and 14.

Calculating the median:
\[ \text{Median} = \frac{9 + 14}{2} = \frac{23}{2} = 11.5 \]

### Step 3: Determine Q1 (First Quartile)
Q1 is the median of the lower half of the data. The lower half consists of the first two numbers: 7 and 9.

Calculating Q1:
\[ Q1 = \frac{7 + 9}{2} = \frac{16}{2} = 8 \]

### Step 4: Determine Q3 (Third Quartile)
Q3 is the median of the upper half of the data. The upper half consists of the last two numbers: 14 and 19.

Calculating Q3:
\[ Q3 = \frac{14 + 19}{2} = \frac{33}{2} = 16.5 \]

### Step 5: Calculate the Inter-Quartile Range (IQR)
The inter-quartile range is calculated as:
\[ IQR = Q3 - Q1 \]
Substituting the values we found:
\[ IQR = 16.5 - 8 = 8.5 \]

### Final Answer
The inter-quartile range for the given data is:
\[ \boxed{8.5} \]

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