Describe in detail what you need	The following is a record of the total hours of tutorials in a study center in 11 months of 2024: 35, 31, 29, 28, 31, 27, 33, 32, 39, 31, 29. What is the first, second and third quartiles?
How many pages	1

Quartiles Calculation for Tutorial Hours

To analyze the distribution of tutorial hours at the study center over a span of 11 months in 2024, we will calculate the first, second, and third quartiles based on the provided data set. The hours recorded for each month are as follows:

• Data Set: 35, 31, 29, 28, 31, 27, 33, 32, 39, 31, 29

Step 1: Organizing the Data

Before we can calculate the quartiles, we need to sort the data in ascending order.

• Sorted Data: 27, 28, 29, 29, 31, 31, 31, 32, 33, 35, 39

Step 2: Understanding Quartiles

Quartiles divide a data set into four equal parts:

• Q1 (First Quartile): The median of the first half of the data (25th percentile).
• Q2 (Second Quartile): The median of the entire data set (50th percentile).
• Q3 (Third Quartile): The median of the second half of the data (75th percentile).

Step 3: Finding the Quartiles

Calculation of Q2 (Median)

To find Q2, the median, we determine the middle number in the sorted data:

• The data set has 11 values, so the median is the middle value, which is at position (11 + 1) / 2 = 6.

Thus, Q2 (Median) is:

• Q2 = 31

Calculation of Q1 (First Quartile)

To calculate Q1, we consider the first half of the data:

• First Half: 27, 28, 29, 29, 31

Since there are 5 values, the median is the middle value at position (5 + 1) / 2 = 3.

Thus, Q1 is:

• Q1 = 29

Calculation of Q3 (Third Quartile)

Next, we focus on the second half of the data:

• Second Half: 31, 31, 32, 33, 35, 39

With 6 values in this set, we find the median by taking the average of the 3rd and 4th values (positions 3 and 4):

Values: 31, 31, 32, 33, 35, 39

So, ( Q3 ) is calculated as follows:

• Q3 = (32 + 33) / 2 = 32.5

Summary of Results

The quartiles calculated from the tutorial hours data set are:

• First Quartile (Q1): 29
• Second Quartile (Q2/Median): 31
• Third Quartile (Q3): 32.5

Conclusion

The quartiles provide a valuable summary of the data distribution regarding tutorial hours at the study center. With these values, one can better understand the spread of the tutorial hours and make informed decisions based on this statistical analysis. Understanding the distribution helps in assessing trends over time and setting realistic goals for future tutorial offerings.