10, 17, 19, 5, 26, 24, 12, 21, 15, 7

Middle 30% of the observations lie between:
a) P60 to P90 b) P35 to P65 c)P40 to P70 d) P45 to P75

To determine between which percentiles the middle 30% of the observations lie, we first need to understand what "middle 30%" means in terms of percentiles.

- The middle 30% of a data set will start from the 35th percentile and end at the 65th percentile. This is because the middle 30% represents the central portion of the data, excluding the lower 35% and the upper 35%.
  
So, the correct answer is:

**b) P35 to P65**

Would you like any further details on how this was calculated, or do you have any other questions? Here are some related questions you might find interesting:

1. How do you calculate percentiles in a data set?
2. What is the significance of the interquartile range in statistics?
3. How can you determine the quartiles of a given data set?
4. What is the difference between percentiles and quartiles?
5. How do percentiles help in understanding the distribution of data?

**Tip:** Remember, percentiles divide your data into 100 equal parts, so knowing how to calculate them can help you understand the spread and distribution of your data better.

Discover how to determine the middle 30% of observations in a dataset using percentiles. This problem focuses on statistical analysis, specifically understanding percentiles and their application in data interpretation. Suitable for students in Grades 10-12.

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