some researchers developing a new intelligence test are trying to decide the maximum time to allow for completion of the test. the researchers have recorded the time for completion of the test for each of 28 participants who took the test for practice. the histogram below summarizes the completion time information for these 28 participants.

based on the histogram, estimate the mean time for completion (in seconds) for the participants. carry your intermediate computations to at least four decimal places, and round your answer to at least one decimal place.

Question

some researchers developing a new intelligence test are trying to decide the maximum time to allow for completion of the test. the researchers have recorded the time for completion of the test for each of 28 participants who took the test for practice. the histogram below summarizes the completion time information for these 28 participants.

based on the histogram, estimate the mean time for completion (in seconds) for the participants. carry your intermediate computations to at least four decimal places, and round your answer to at least one decimal place.

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": [ "Histogram Interpretation", "Grouped Data Mean Estimation" ], "new_concepts": [], "current_concepts": [ "Histogram Interpretation", "Grouped Data Mean Estimation" ] } ## Identify class intervals and frequencies Using the **Histogram Interpretation** knowledge point $$ \begin{array}{c|c} \text{Interval} & \text{Frequency } (f) \ \hline 500 - 700 & 8 \ 700 - 900 & 8 \ 900 - 1100 & 6 \ 1100 - 1300 & 4 \ 1300 - 1500 & 2 \ \end{array} $$ ## Calculate class midpoints Using the **Grouped Data Mean Estimation** knowledge point $$ \begin{aligned} M_1 &= \frac{500 + 700}{2} = 600 \ M_2 &= \frac{700 + 900}{2} = 800 \ M_3 &= \frac{900 + 1100}{2} = 1000 \ M_4 &= \frac{1100 + 1300}{2} = 1200 \ M_5 &= \frac{1300 + 1500}{2} = 1400 \end{aligned} $$ ## Compute sum of products Using the **Grouped Data Mean Estimation** knowledge point $$ \begin{aligned} \sum (f \cdot M) &= (8 \cdot 600) + (8 \cdot 800) + (6 \cdot 1000) + (4 \cdot 1200) + (2 \cdot 1400) \ &= 4800 + 6400 + 6000 + 4800 + 2800 \ &= 24800 \end{aligned} $$ ## Calculate estimated mean Using the **Grouped Data Mean Estimation** knowledge point $$ \begin{aligned} n &= 8 + 8 + 6 + 4 + 2 = 28 \ \bar{x} &\approx \frac{24800}{28} \approx 885.7143 \end{aligned} $$ Based on the histogram, estimate the mean time for completion (in seconds) for the participants. Carry your intermediate computations to at least four decimal places, and round your answer to at least one decimal place. 885.7 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Grouped Data Mean Estimation" ] }

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QUESTION IMAGE

Question

Explanation:

Identify class intervals and frequencies

Calculate class midpoints

Compute sum of products

Calculate estimated mean

Answer: