mean temperature: $78^\circ$
standard deviation: $5^\circ$

check all of the temperatures that are within one standard deviation of the mean
x $72^\circ$
v $74^\circ$
v $79^\circ$
x $84^\circ$

how many years had temperatures that were exactly one standard deviation from the mean?

Question

mean temperature: $78^\circ$
standard deviation: $5^\circ$

check all of the temperatures that are within one standard deviation of the mean
x $72^\circ$
v $74^\circ$
v $79^\circ$
x $84^\circ$

how many years had temperatures that were exactly one standard deviation from the mean?

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Standard Deviation Interval" ], "new_concepts": [], "current_concepts": [ "Standard Deviation Interval", "Graph Interpretation" ] } ## Identify the mean and standard deviation Using the *Standard Deviation Interval* knowledge point $$ \begin{aligned} \mu &= 78^\circ \ \sigma &= 5^\circ \end{aligned} $$ ## Calculate the target temperatures Using the *Standard Deviation Interval* knowledge point $$ \begin{aligned} \text{Target Temperatures} &= \mu \pm \sigma \ &= 78^\circ \pm 5^\circ \ &= \{73^\circ, 83^\circ\} \end{aligned} $$ ## Count the occurrences of target temperatures from the dot plot We locate the values $73^\circ$ and $83^\circ$ on the horizontal axis of the dot plot and count the number of dots (years) above each: - At $73^\circ$: There are $4$ dots. - At $83^\circ$: There are $4$ dots. ## Sum the total number of years $$ \begin{aligned} \text{Total Years} &= 4 + 4 \ &= 8 \end{aligned} $$ How many years had temperatures that were exactly one standard deviation from the mean? 8 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Standard Deviation Interval" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the mean and standard deviation

Calculate the target temperatures

Count the occurrences of target temperatures from the dot plot

Sum the total number of years

Answer: