Question 4
The following set of data is from a sample.

Compute the standard deviation:
Add your answer
Integer, decimal, or E notation allowed

Question

Question 4 The following set of data is from a sample. $$ 10,14,5,13,11,14,3 $$ Compute the standard deviation: Add your answer Integer, decimal, or E notation allowed

UpStudy AI · Accepted Answer

To calculate the **standard deviation** for the given sample data:

$$ 10, 14, 5, 13, 11, 14, 3 $$

We'll follow these steps:

1. **Calculate the Mean ($$\mu$$)**:
   
   $$
   \mu = \frac{10 + 14 + 5 + 13 + 11 + 14 + 3}{7} = \frac{70}{7} = 10
   $$

2. **Compute Each Deviation from the Mean and Square It**:
   
   $$
   \begin{align*}
   (10 - 10)^2 &= 0 \
   (14 - 10)^2 &= 16 \
   (5 - 10)^2 &= 25 \
   (13 - 10)^2 &= 9 \
   (11 - 10)^2 &= 1 \
   (14 - 10)^2 &= 16 \
   (3 - 10)^2 &= 49 \
   \end{align*}
   $$

3. **Sum of Squared Deviations**:
   
   $$
   0 + 16 + 25 + 9 + 1 + 16 + 49 = 116
   $$

4. **Calculate the Sample Variance ($$s^2$$)**:
   
   Since this is a sample, we use $$n-1$$ as the denominator:
   
   $$
   s^2 = \frac{116}{7-1} = \frac{116}{6} \approx 19.3333
   $$

5. **Compute the Standard Deviation ($$s$$)**:
   
   $$
   s = \sqrt{19.3333} \approx 4.397
   $$

**Final Answer:**  
The standard deviation is approximately **4.397**.
The standard deviation is approximately 4.397.

Question 4
The following set of data is from a sample.

Compute the standard deviation:
Add your answer
Integer, decimal, or E notation allowed

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Question 4 The following set of data is from a sample. Compute the standard deviation: Add your answer Integer, decimal, or E notation allowed

Upstudy AI Solution

Answer

Solution

Extra Insights

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Latest Statistics Questions

Question 4
The following set of data is from a sample.

Compute the standard deviation:
Add your answer
Integer, decimal, or E notation allowed