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 median, mean?
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Statistical Analysis of Tutorial Hours in a Study Center

In this analysis, we will calculate the median and mean of the total hours of tutorials recorded over 11 months in a study center for the year 2024. The data we have is as follows:

• Hours of Tutorials: 35, 31, 29, 28, 31, 27, 33, 32, 39, 31, 29

Step 1: Organizing the Data

First, we will organize the given data in ascending order:

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

Step 2: Calculating the Median

To find the median, we need to determine the middle value of the ordered data. Since we have 11 data points (which is an odd number), the median will be the value located at the position ((N + 1) / 2), where (N) is the number of data points.

• Median Position:

  [ \text{Median Position} = \frac{11 + 1}{2} = 6 ]

Consequently, the 6th value in our sorted list is 31. Therefore, the median of the total hours of tutorials is 31.

Step 3: Calculating the Mean

The mean (average) is calculated by summing all values and then dividing by the number of values.

• Sum of Hours:

  [ 27 + 28 + 29 + 29 + 31 + 31 + 31 + 32 + 33 + 35 + 39 ]

Calculating the sum:

• ( 27 + 28 = 55 )
• ( 55 + 29 = 84 )
• ( 84 + 29 = 113 )
• ( 113 + 31 = 144 )
• ( 144 + 31 = 175 )
• ( 175 + 31 = 206 )
• ( 206 + 32 = 238 )
• ( 238 + 33 = 271 )
• ( 271 + 35 = 306 )
• ( 306 + 39 = 345 )

Thus, the total hours is 345.

Next, we find the mean:

• Mean Calculation:

  [ \text{Mean} = \frac{\text{Total Hours}}{N} = \frac{345}{11} \approx 31.36 ]

Therefore, the mean of the total hours of tutorials is approximately 31.36.

Conclusion

To summarize our findings:

• Median: 31
• Mean: Approximately 31.36

This statistical analysis provides insight into the distribution of tutorial hours in the study center over the specified 11 months. The median indicates the middle point of the dataset, while the mean gives a sense of the average across all months. Together, these measures help to better understand the performance and usage of the study center's resources throughout the year 2024.