The question in the image is asking to calculate the five-number summary for a given data set.

The data set:

$0, 2, 2, 4, 5, 5, 5, 5, 7, 11$

Step-by-step five-number summary:

1. Minimum: The smallest number in the data set. $\text{Minimum} = 0$

2. First Quartile (Q1): The median of the lower half of the data (excluding the overall median). The lower half is $0, 2, 2, 4, 5$.

   • The median of this set is $2$ (second value). $Q1 = 2$

3. Median (Q2): The middle number of the data set. Since there are 10 data points, the median is the average of the 5th and 6th values, which are both $5$. $Q2 = 5$

4. Third Quartile (Q3): The median of the upper half of the data (excluding the overall median). The upper half is $5, 5, 5, 7, 11$.

   • The median of this set is $5$. $Q3 = 5$

5. Maximum: The largest number in the data set. $\text{Maximum} = 11$

The five-number summary is:

$\text{Five-number summary} = 0, 2, 5, 5, 11$

Now for part b, the minimum value (0) is removed, so the new data set becomes: $2, 2, 4, 5, 5, 5, 5, 7, 11$.

Recalculating the five-number summary:

1. Minimum: $\text{Minimum} = 2$

2. First Quartile (Q1): The lower half is $2, 2, 4, 5$. The median of this set is $3$ (average of $2$ and $4$). $Q1 = 3$

3. Median (Q2): The median of the data set is the middle value, which is $5$. $Q2 = 5$

4. Third Quartile (Q3): The upper half is $5, 5, 7, 11$. The median of this set is $6$ (average of $5$ and $7$). $Q3 = 6$

5. Maximum: $\text{Maximum} = 11$

The new five-number summary is:

$\text{Five-number summary without 0} = 2, 3, 5, 6, 11$

Let me know if you'd like further details or explanations.

Here are 5 related questions:

1. How does the five-number summary help in understanding the distribution of data?
2. What is the significance of the median in a five-number summary?
3. How do outliers affect the five-number summary?
4. Can you calculate the interquartile range (IQR) from the five-number summary?
5. What would the five-number summary look like for a different data set?

Tip: The interquartile range (IQR) is a useful measure of spread and is calculated as $Q3 - Q1$.