The image contains a problem asking for the upper quartile (Q3) of a dataset. The dataset provided is the scores of 10 students who took a final exam:

68, 72, 74, 79, 84, 40, 74, 81, 76, 67.

Steps to find the Upper Quartile (Q3):

1. Sort the Data: The first step is to arrange the data in ascending order: $40, 67, 68, 72, 74, 74, 76, 79, 81, 84$

2. Divide the Data into Quarters:

   • The data has 10 values, so the median (Q2) is between the 5th and 6th values (74 and 74).
   • The lower half (excluding the median) is $40, 67, 68, 72, 74$, and the upper half is $74, 76, 79, 81, 84$.

3. Determine Q3:

   • Q3 is the median of the upper half. The upper half data is $74, 76, 79, 81, 84$.
   • The median of this subset is the middle value, which is 79.

Conclusion:

The upper quartile (Q3) of the dataset is 79.

Would you like to know more details or have any questions?

Here are some related questions to consider:

1. What is the lower quartile (Q1) of the dataset?
2. How do you calculate the interquartile range (IQR) and what is it for this dataset?
3. How would the upper quartile change if the highest score were increased to 90?
4. How do quartiles help in understanding the spread of the data?
5. How can you use quartiles to detect outliers in the dataset?

Tip: Quartiles are essential in understanding the distribution of data. They divide your data into four parts, each containing 25% of the data, making them useful for detecting spread and central tendency.