Let's work through the problem step by step using the scores provided:

The scores obtained by 11 students are: $8, 12, 14, 15, 14, 1, 19, 26, 17, 33, 17$

Step 1: Sort the data

To find the quartiles and other statistics, we first need to sort the data in ascending order:

$1, 8, 12, 14, 14, 15, 17, 17, 19, 26, 33$

Step 2: Calculate the Median (Q2)

Since there are 11 data points, the median will be the middle value, which is the 6th value in the sorted list:

Median (Q2) = 15

Step 3: Calculate the First Quartile (Q1)

The first quartile (Q1) is the median of the lower half of the data. This excludes the median itself, so we consider the first 5 numbers: $1, 8, 12, 14, 14$ The median of these values is the third number:

First Quartile (Q1) = 12

Step 4: Calculate the Third Quartile (Q3)

The third quartile (Q3) is the median of the upper half of the data. This excludes the median itself, so we consider the last 5 numbers: $17, 17, 19, 26, 33$ The median of these values is the third number:

Third Quartile (Q3) = 19

Step 5: Calculate the Range

The range is the difference between the highest and lowest values in the data set:

Range = $33 - 1 = 32$

Step 6: Calculate the Interquartile Range (IQR)

The interquartile range (IQR) is the difference between the third quartile and the first quartile:

IQR = $Q3 - Q1 = 19 - 12 = 7$

Final Summary:

• First Quartile (Q1) = 12
• Median (Q2) = 15
• Third Quartile (Q3) = 19
• Range = 32
• Interquartile Range (IQR) = 7

Let me know if you'd like further details or clarification on any of the steps!

Here are 5 related questions:

1. How do you calculate the quartiles for a larger data set?
2. What is the significance of the interquartile range in statistics?
3. Can the quartiles be influenced by outliers in the data set?
4. How do you calculate quartiles in grouped data?
5. What is the difference between range and interquartile range?

Tip: When dealing with quartiles, always ensure your data set is sorted in ascending order before proceeding with the calculations!