\begin{tabular}{l} Question 6 \ The following set of data is from a sample. \ 10, 14, $$ 5,13,11,14,3 $$ \ Compute the Variance: \ \hline Add your answer \ Integer, decimal, or E notation allowed \end{tabular}

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UpStudy AI · Accepted Answer

To compute the **sample variance** for the given data set:

**Data:** 10, 14, 5, 13, 11, 14, 3

**Step 1: Calculate the Mean**

$$
\text{Mean} (\bar{x}) = \frac{10 + 14 + 5 + 13 + 11 + 14 + 3}{7} = \frac{70}{7} = 10
$$

**Step 2: Compute Each Squared Deviation from the Mean**

$$
\begin{align*}
(10 - 10)^2 &= 0 \
(14 - 10)^2 &= 16 \
(5 - 10)^2 &= 25 \
(13 - 10)^2 &= 9 \
(11 - 10)^2 &= 1 \
(14 - 10)^2 &= 16 \
(3 - 10)^2 &= 49 \
\end{align*}
$$

**Step 3: Sum of Squared Deviations**

$$
0 + 16 + 25 + 9 + 1 + 16 + 49 = 116
$$

**Step 4: Calculate the Sample Variance**

$$
s^2 = \frac{\text{Sum of Squared Deviations}}{n - 1} = \frac{116}{7 - 1} = \frac{116}{6} \approx 19.333
$$

**Answer:**  
19.333
The sample variance is approximately 19.333.

Question 6

The following set of data is from a sample.

10, 14,

Compute the Variance:

Add your answer

Integer, decimal, or E notation allowed

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Question 6 The following set of data is from a sample. 10, 14, Compute the Variance: Add your answer Integer, decimal, or E notation allowed