Determine the estimated score in GECMAT if the number of hours spent in studying is 5 hours? 20 minutes? Show your complete solution and make analysis of your answer.

Understand the Problem

The question requires us to analyze a dataset relating scores to hours spent studying and then estimate a score based on a given study time. The necessary approach will involve possibly calculating an average score per hour and using it to find the score for the specified number of hours studied.

Answer

The estimated score is approximately $32.7$.

Steps to Solve

Organize the Data

List the scores and corresponding hours spent in studying as pairs:

(27, 2.6)
(24, 3.2)
(23, 3)
(29, 5)
(29, 0.8)
(24, 0.4)
(27, 5.2)
(24, 4.1)
(27, 3.8)
(25, 1.5)
(28, 4)
(16, 3.3)
(22, 1.2)
(30, 2.6)
(22, 4.6)

Calculate the Average Score per Hour

Using the formula for the average score for each data point, we can find the average score per hour across all pairs:

$$ \text{Average Score} = \frac{\text{Total Scores}}{\text{Total Hours}} $$

Total scores: $27 + 24 + 23 + 29 + 29 + 24 + 27 + 24 + 27 + 25 + 28 + 16 + 22 + 30 + 22$
Total hours: $2.6 + 3.2 + 3 + 5 + 0.8 + 0.4 + 5.2 + 4.1 + 3.8 + 1.5 + 4 + 3.3 + 1.2 + 2.6 + 4.6$

Sum Up Total Scores and Hours

Calculating the total scores:

$$ \text{Total Scores} = 27 + 24 + 23 + 29 + 29 + 24 + 27 + 24 + 27 + 25 + 28 + 16 + 22 + 30 + 22 = 388 $$

Calculating the total hours:

$$ \text{Total Hours} = 2.6 + 3.2 + 3 + 5 + 0.8 + 0.4 + 5.2 + 4.1 + 3.8 + 1.5 + 4 + 3.3 + 1.2 + 2.6 + 4.6 = 63.3 $$

Calculate the Average

Now use the totals to find the average score per hour:

$$ \text{Average Score per Hour} = \frac{388}{63.3} \approx 6.13 $$

Estimate the Score for 5 hours 20 minutes

Convert 5 hours 20 minutes into hours:

$$ 5 \text{ hours } 20 \text{ minutes} = 5 + \frac{20}{60} \approx 5.33 \text{ hours} $$

Then calculate the estimated score using the average score per hour:

$$ \text{Estimated Score} = 6.13 \times 5.33 \approx 32.7 $$

The estimated score for 5 hours and 20 minutes of studying is approximately $32.7$.

More Information

This scoring estimation method assumes a linear relationship between hours studied and scores achieved. Depending on the dataset, actual scores can vary significantly based on various factors, including individual learning differences and prior knowledge.

Tips

Forgetting to convert minutes into hours can lead to incorrect calculations.
Miscalculating total scores or total hours may skew the average.

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