The problem asks to calculate the first quartile (Q1) for the given data set:

Data Set: 12, 7, 5, 18, 10, 14, 9, 15, 6, 11

Steps to Calculate the First Quartile (Q1):

1. Order the Data Set: Arrange the data in ascending order.

   • Ordered Data Set: 5, 6, 7, 9, 10, 11, 12, 14, 15, 18

2. Determine the Position of Q1: The first quartile (Q1) is the median of the lower half of the data.

   • Total number of data points (n) = 10
   • The lower half consists of the first 5 data points: 5, 6, 7, 9, 10

3. Find Q1: Since the number of observations in the lower half is odd (5), the median is the third value in the lower half.

   • Q1 = 7

Final Answer:

The first quartile (Q1) is 7.

Would you like a detailed explanation of any part of this process?

Here are 5 relative questions to expand your understanding:

1. How do you calculate the third quartile (Q3) for this data set?
2. What is the median of the entire data set?
3. How does the interquartile range (IQR) relate to Q1 and Q3?
4. What steps would you take to find the first quartile if the number of data points was odd?
5. How does the calculation of Q1 change for a larger data set?

Tip: Always ensure that the data is ordered correctly before calculating quartiles or any statistical measure.