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For the data given the inter-quartile ra...

For the data given the inter-quartile range is

A

7

B

19

C

14

D

9

Text Solution

AI Generated Solution

The correct Answer is:
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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