The inter - quartile range of the data 1, 3, 5, 7, 9, 11, 13, 15, 17, 19

Options

A. 2
B. 4
C. 6
D. 10

Answer

To find the inter-quartile range (IQR) of the given data set: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, follow these steps:

### Step 1: Organize the Data
The data is already organized in ascending order:
1, 3, 5, 7, 9, 11, 13, 15, 17, 19

### Step 2: Determine the Number of Data Points
Count the number of data points (n):
- Here, n = 10.

### Step 3: Find the Median
To find the median of the dataset:
- Since n is even, the median is the average of the two middle numbers.
- The two middle numbers are the 5th and 6th terms: 9 and 11.
- Median = (9 + 11) / 2 = 20 / 2 = 10.

### Step 4: Divide the Data into Two Halves
Now, divide the data into two halves:
- Lower half (Q1): 1, 3, 5, 7, 9
- Upper half (Q3): 11, 13, 15, 17, 19

### Step 5: Find Q1 (First Quartile)
To find Q1, calculate the median of the lower half:
- The lower half has 5 data points, so the median is the 3rd term, which is 5.

### Step 6: Find Q3 (Third Quartile)
To find Q3, calculate the median of the upper half:
- The upper half also has 5 data points, so the median is the 3rd term, which is 15.

### Step 7: Calculate the Inter-Quartile Range (IQR)
Now, use the formula for IQR:
- IQR = Q3 - Q1 = 15 - 5 = 10.

### Conclusion
The inter-quartile range (IQR) of the data set is 10.

---