Consider the following sample of five measurements.
2 comma 3 comma 1 comma 0 comma 4   
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Part 1
a. Calculate the​ range, s squared​, and s.
rangeequals
  
enter your response here
Part 2
s squaredequals
  
enter your response here ​(Round to one decimal place as​ needed.)
Part 3
sequals
  
enter your response here ​(Round to two decimal places as​ needed.)

Let's calculate the required statistical measures step by step.

### **Given Data:**  
\( 2, 3, 1, 0, 4 \)

---

### **Part 1: Range**
The range is calculated as:  
\[
\text{Range} = \text{Maximum value} - \text{Minimum value}
\]

\[
\text{Range} = 4 - 0 = 4
\]

**Answer:** \( \mathbf{4} \)

---

### **Part 2: Variance (\( s^2 \))**  
Sample variance is calculated using the formula:

\[
s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1}
\]

#### **Step 1: Compute the Mean (\(\bar{x}\))**  
\[
\bar{x} = \frac{2 + 3 + 1 + 0 + 4}{5} = \frac{10}{5} = 2
\]

#### **Step 2: Compute Each Deviation Squared**  
\[
(2 - 2)^2 = 0
\]
\[
(3 - 2)^2 = 1
\]
\[
(1 - 2)^2 = 1
\]
\[
(0 - 2)^2 = 4
\]
\[
(4 - 2)^2 = 4
\]

#### **Step 3: Compute Sample Variance**
\[
s^2 = \frac{0 + 1 + 1 + 4 + 4}{5 - 1} = \frac{10}{4} = 2.5
\]

**Answer:** \( \mathbf{2.5} \) (rounded to one decimal place)

---

### **Part 3: Standard Deviation (\( s \))**  
Standard deviation is the square root of variance:

\[
s = \sqrt{s^2} = \sqrt{2.5}
\]

\[
s \approx 1.58
\]

**Answer:** \( \mathbf{1.58} \) (rounded to two decimal places)

---

### **Final Answers:**
- **Range:** \( 4 \)
- **Variance (\( s^2 \))**: \( 2.5 \)
- **Standard Deviation (\( s \))**: \( 1.58 \)

Would you like a further breakdown or another example?

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### **Related Questions:**
1. What is the difference between sample variance and population variance?
2. How does increasing the sample size affect the standard deviation?
3. Can the standard deviation ever be negative? Why or why not?
4. How do outliers impact the range, variance, and standard deviation?
5. What are the applications of standard deviation in real-world scenarios?

**Tip:** The standard deviation is always in the same unit as the data, while the variance is in squared units.

Consider the following sample of five measurements. 2, 3, 1, 0, 4. Calculate the range, s squared, and s.

Learn how to calculate the range, sample variance (s²), and sample standard deviation (s) using a sample dataset of five measurements: 2, 3, 1, 0, and 4. This step-by-step guide includes the required formulas and detailed calculations. Suitable for students in Grades 9-11.

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