In the data set below, what is the variance? 9, 4, 3, 3, 3, 7, 6 If the answer is a decimal, round it to the nearest tenth. variance (σ^2): _____

Calculate Mean: Calculate the mean of the data set. question_prompt: What is the variance of the given data set? Data set: 9, 4, 3, 3, 3, 7, 6 Mean μ = (9 + 4 + 3 + 3 + 3 + 7 + 6)/7 μ = 35/7 μ = 5Squared Differences: Calculate the squared differences from the mean for each data point. Data set: 9, 4, 3, 3, 3, 7, 6 Mean μ = 5 Squared differences: (9 - 5)^2, (4 - 5)^2, (3 - 5)^2, (3 - 5)^2, (3 - 5)^2, (7 - 5)^2, (6 - 5)^2 = 4^2, (-1)^2, (-2)^2, (-2)^2, (-2)^2, 2^2, 1^2 = 16, 1, 4, 4, 4, 4, 1Sum Squared Differences: Sum the squared differences to find Σ(x_i - μ)^2. Sum: 16 + 1 + 4 + 4 + 4 + 4 + 1 = 34Calculate Variance: Calculate the variance using the formula σ^2 = (Σ(x_i - μ)^2)/N. Number of data points N = 7 Variance σ^2 = 34/7 σ^2 ≈ 4.857 Round to the nearest tenth: σ^2 ≈ 4.9

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In the data set below, what is the variance? $\newline$ $9, 4, 3, 3, 3, 7, 6$ $\newline$ If the answer is a decimal, round it to the nearest tenth. $\newline$ variance $(\sigma^2)$ : _____

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Algebra 1

Variance and standard deviation

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Q. In the data set below, what is the variance?

\newline

9, 4, 3, 3, 3, 7, 6

\newline

If the answer is a decimal, round it to the nearest tenth.

\newline

variance

(\sigma^2)

: _____

Calculate Mean: Calculate the mean of the data set. $\newline$ question_prompt: What is the variance of the given data set? $\newline$ Data set: $9, 4, 3, 3, 3, 7, 6$ $\newline$ Mean $\mu = (9 + 4 + 3 + 3 + 3 + 7 + 6)/7$ $\newline$ $\mu = 35/7$ $\newline$ $\mu = 5$
Squared Differences: Calculate the squared differences from the mean for each data point. $\newline$ Data set: $9, 4, 3, 3, 3, 7, 6$ $\newline$ Mean $\mu = 5$ $\newline$ Squared differences: $(9 - 5)^2, (4 - 5)^2, (3 - 5)^2, (3 - 5)^2, (3 - 5)^2, (7 - 5)^2, (6 - 5)^2$ $\newline$ $= 4^2, (-1)^2, (-2)^2, (-2)^2, (-2)^2, 2^2, 1^2$ $\newline$ $= 16, 1, 4, 4, 4, 4, 1$
Sum Squared Differences: Sum the squared differences to find $\Sigma(x_i - \mu)^2$ . $\newline$ Sum: $16 + 1 + 4 + 4 + 4 + 4 + 1$ $\newline$ = $34$
Calculate Variance: Calculate the variance using the formula $\sigma^2 = \frac{\Sigma(x_i - \mu)^2}{N}$ . $\newline$ Number of data points $N = 7$ $\newline$ Variance $\sigma^2 = \frac{34}{7}$ $\newline$ $\sigma^2 \approx 4.857$ $\newline$ Round to the nearest tenth: $\sigma^2 \approx 4.9$