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{ "quality": "blurry", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Basic Statistics" ], "new_concepts": [ "Population Variance Calculation" ], "current_concepts": [ "Basic Statistics", "Population Variance Calculation" ] } ## Calculate the mean of the data set Using the *Basic Statistics* knowledge point $$ \mu = 7,\quad N = 12 $$ ## Calculate the sum of squared deviations Using the *Basic Statistics* knowledge point $$ \begin{aligned} \sum (x_i - \mu)^2 = &(1.8-7)^2 + (2.5-7)^2 + (2.6-7)^2 + (4.4-7)^2 + (4.4-7)^2 + (7.3-7)^2 \ &+ (8.0-7)^2 + (9.5-7)^2 + (10.3-7)^2 + (10.4-7)^2 + (11.1-7)^2 + (11.7-7)^2 \end{aligned} $$ $$ \begin{aligned} \sum (x_i - \mu)^2 = &(-5.2)^2 + (-4.5)^2 + (-4.4)^2 + (-2.6)^2 + (-2.6)^2 + (0.3)^2 \ &+ (1.0)^2 + (2.5)^2 + (3.3)^2 + (3.4)^2 + (4.1)^2 + (4.7)^2 \end{aligned} $$ $$ \begin{aligned} \sum (x_i - \mu)^2 = &27.04 + 20.25 + 19.36 + 6.76 + 6.76 + 0.09 \ &+ 1.00 + 6.25 + 10.89 + 11.56 + 16.81 + 22.09 \end{aligned} $$ $$ \sum (x_i - \mu)^2 = 148.86 $$ ## Calculate the population variance Using the *Basic Statistics* knowledge point $$ \sigma^2 = \frac{\sum (x_i - \mu)^2}{N} = \frac{148.86}{12} = 12.405 $$

0

3.217

3.522

12.405

148.86

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Population Variance Calculation" ] }

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Explanation:

Calculate the mean of the data set

Calculate the sum of squared deviations

Calculate the population variance

Answer: