the graph shows the distribution of hand lengths, in centimeters, of the members of an orchestra.

what is the variance of the data?

Question

the graph shows the distribution of hand lengths, in centimeters, of the members of an orchestra.

what is the variance of the data?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Normal Distribution", "Standard Deviation", "Variance Calculation" ], "new_concepts": [], "current_concepts": [ "Normal Distribution", "Standard Deviation", "Variance Calculation" ] } ## Identify the mean and inflection points Using the *Normal Distribution* knowledge point $$ \begin{aligned} &\mu = 19\ &\text{Inflection points at } x = 17 \text{ and } x = 21 \end{aligned} $$ ## Determine the standard deviation Using the *Standard Deviation* knowledge point $$ \begin{aligned} &\sigma = 21 - 19 = 2\ &\sigma = 19 - 17 = 2 \end{aligned} $$ ## Calculate the variance Using the *Variance Calculation* knowledge point $$ \begin{aligned} &\sigma^2 = 2^2 = 4 \end{aligned} $$

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{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Normal Distribution" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the mean and inflection points

Determine the standard deviation

Calculate the variance

Answer: