(b)Find the third quartile of the scores.

The third quartile of the scores is 






To find the third quartile (Q3) of the scores, you can follow a similar process to that used for finding the first quartile:

1. **Determine the position of the third quartile (Q3)**:
   - The third quartile (Q3) is the 75th percentile of the data.
   - The formula to find the position \( P \) of Q3 in an ordered data set is:
     \[
     P = \frac{3(n+1)}{4}
     \]
     where \( n \) is the number of data points.

2. **Calculate the position**:
   - Here, \( n = 29 \).
   - So, \( P = \frac{3(29+1)}{4} = \frac{90}{4} = 22.5 \).

3. **Interpret the position**:
   - Since 22.5 is not an integer, the third quartile will be the average of the 22nd and 23rd data points.

4. **Find the 22nd and 23rd data points**:
   - The 22nd data point is 88, and the 23rd data point is 90.

5. **Calculate Q3**:
   \[
   Q3 = \frac{88 + 90}{2} = \frac{178}{2} = 89
   \]

Thus, the third quartile (Q3) of the scores is **89**.

Would you like more details or have any questions? Here are some related questions to expand your understanding:

1. How does the third quartile compare to the mean of this data set?
2. How do you determine if a data set is skewed based on its quartiles?
3. What are the implications of a higher third quartile in a data set?
4. How can you use Q3 to identify outliers in this data set?
5. How would the quartiles change if a new score, say 100, was added to the data set?

**Tip:** Quartiles are key in identifying the spread and central tendency of data. Q3 is particularly useful in understanding the upper spread of the data set.

Discover how to find the third quartile (Q3) of scores with a detailed step-by-step guide. This problem involves calculating percentiles and quartiles in statistics. Suitable for high school students and anyone interested in data analysis.

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