To calculate the first quartile (Q₁), third quartile (Q₃), and interquartile range (IQR), we need to follow these steps:

Data Set:

9, 23, 39, 14, 7, 32, 12, 22, 34, 15

Step 1: Sort the data in ascending order.

7, 9, 12, 14, 15, 22, 23, 32, 34, 39

Step 2: Find Q₁ (First Quartile)

• The first quartile (Q₁) is the median of the lower half of the data. To find this, we look at the numbers below the median.

Lower half of the dataTo calculate the first quartile (Q₁), third quartile (Q₃), and interquartile range (IQR), we need to follow these steps:

Data Set:

9, 23, 39, 14, 7, 32, 12, 22, 34, 15

Step 1: Sort the data in ascending order.

7, 9, 12, 14, 15, 22, 23, 32, 34, 39

Step 2: Find Q₁ (First Quartile)

• The first quartile (Q₁) is the median of the lower half of the data. To find this, we look at the numbers below the median.

Lower half of the 7, 9, 12, 14, 15

• Median of this half (Q₁): The middle value is 12.

Thus, Q₁ = 12.

Step 3: Find Q₃ (Third Quartile)

• The third quartile (Q₃) is the median of the upper half of the data.

Upper half of the dataTo calculate the first quartile (Q₁), third quartile (Q₃), and interquartile range (IQR), we need to follow these steps:

Data Set:

9, 23, 39, 14, 7, 32, 12, 22, 34, 15

Step 1: Sort the data in ascending order.

7, 9, 12, 14, 15, 22, 23, 32, 34, 39

Step 2: Find Q₁ (First Quartile)

• The first quartile (Q₁) is the median of the lower half of the data. To find this, we look at the numbers below the median.

Lower half of the 7, 9, 12, 14, 15

• Median of this half (Q₁): The middle value is 12.

Thus, Q₁ = 12.

Step 3: Find Q₃ (Third Quartile)

• The third quartile (Q₃) is the median of the upper half of the data.

Upper half of the 22, 23, 32, 34, 39

• Median of this half (Q₃): The middle value is 32.

Thus, Q₃ = 32.

Step 4: Find the IQR (Interquartile Range)

• The IQR is the difference between Q₃ and Q₁.

$\text{IQR} = Q₃ - Q₁ = 32 - 12 = 20$

Final Answer:

• First Quartile (Q₁) = 12
• Third Quartile (Q₃) = 32
• Interquartile Range (IQR) = 20

Would you like more details on this, or do you have any further questions?

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Here are 5 related questions for practice:

1. How do you find the median of a data set?
2. What is the significance of the interquartile range in statistics?
3. How do outliers affect the quartiles and IQR?
4. Can the IQR be used to identify outliers? How?
5. What is the difference between the mean and median in a skewed distribution?

Tip: Always sort the data before calculating quartiles or medians!