X1.74622.42912.39781.82952.09561.98012.06381.98621.81921.82211.94182.0916Based on the above table,Find the Inter-Quartile range:

1. Break Down the Problem

To find the Inter-Quartile Range (IQR), we need to follow these steps:

1. Organize the data in ascending order.
2. Calculate the first quartile (Q1) and the third quartile (Q3).
3. Subtract Q1 from Q3 to find the IQR.

2. Relevant Concepts

• First Quartile (Q1) is the median of the first half of the data.
• Third Quartile (Q3) is the median of the second half of the data.
• Inter-Quartile Range (IQR) is calculated as: $IQR = Q3 - Q1$

3. Analysis and Detail

First, let's rewrite the given data for clarity:

• Data Points: 1.7462, 2.4291, 2.3978, 1.8295, 2.0956, 1.9801, 2.0638, 1.9862, 1.8192, 1.8221, 1.9418, 2.0916

Step 1: Organize the Data

• Sorted Data: 1.7462, 1.7801, 1.8221, 1.8295, 1.9418, 2.0638, 2.0956, 2.3978, 2.4291, 2.0916

Step 2: Find Quartiles

• The number of data points $n = 12$.
• The first half (1 to 6): 1.7462, 1.8295, 1.9418, 1.9801, 2.0638, 2.0956
• The second half (7 to 12): 2.0916, 2.3978, 2.4291

Calculating Q1:

• Q1 is the median of the first half: $Q1 = \frac{1.8295 + 1.9418}{2} = 1.88565$

Calculating Q3:

• Q3 is the median of the second half: $Q3 = \frac{2.0956 + 2.3978}{2} = 2.2467$

4. Verify and Summarize

Now calculate the IQR: $IQR = Q3 - Q1 = 2.2467 - 1.88565 = 0.36105$

Final Answer

The Inter-Quartile Range (IQR) is approximately 0.36105.