To answer these new questions, let's analyze the box plot you provided earlier with the specific values in mind:

Recalculated Points Based on the Given Box Plot:

• Minimum (Lower Whisker): 40
• Lower Quartile (Q1): 50
• Median (Q2): 70
• Upper Quartile (Q3): 90
• Maximum (Upper Whisker): 110

Questions:

1. Less than 57%:

   • The 57th percentile is between the median (70) and the first quartile (50). Since the median (70) corresponds to 50% of the data, and Q3 (90) corresponds to 75%, 57% would fall somewhere between 50 and 70. Thus, approximately slightly more than 50% of the data is less than 57.

2. Between 57% and 90%:

   • 57% lies between the median (70) and the third quartile (90). As the range from Q2 (70) to Q3 (90) corresponds to 25% of the data, and 57% is just above 50%, approximately between 7% and 25% of the data falls between 57% and 90%.

3. Less than 90:

   • 90 corresponds to the upper quartile (Q3), so 75% of the data is less than 90.

4. Greater than 78:

   • 78 falls between the median (70) and Q3 (90), meaning it's in the upper 25% of the data distribution. Approximately between 10% and 25% of the data is greater than 78.

Summarized Answers:

a) Less than 57%: Slightly more than 50%
b) Between 57% and 90%: Between 7% and 25%
c) Less than 90: 75%
d) Greater than 78: Between 10% and 25%

Would you like any further explanations or additional questions on this topic?

Related Questions:

1. How can you determine the exact percentile for a given data point using a box plot?
2. What is the significance of the median in a box plot?
3. How can you visually estimate percentiles on a box plot?
4. Why does the interquartile range represent 50% of the data?
5. How can outliers be identified on a box plot?

Tip:

When interpreting a box plot, remember that the percentiles (like 57%) aren't directly shown but can be estimated based on the position relative to the quartiles.