https://file.aiquickdraw.com/mathbot/file/17264361670792n8fhpui.jpg

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 \( Q3 - Q1 \).

What is the five-number summary for the data 0, 2, 2, 4, 5, 5, 5, 5, 7, 11? When the minimum, 0, is removed from the data set, what is the five-number summary?

Learn how to calculate the five-number summary for the data set 0, 2, 2, 4, 5, 5, 5, 5, 7, 11, including minimum, Q1, median, Q3, and maximum. Discover how removing the minimum affects the summary. Ideal for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation