It Is Well-Known That The Relationship Between Degrees And F

It is well-known that the relationship between degree Fahrenheit (F) and degree Celsius (C) is, F =(9/5)*C + 32 We randomly selected 100 days in October from and recorded the temperature (in degree Fahrenheit) of New York City. We have the following summary statistics from R: Min. 1st Qu. Median Mean 3rd Qu. Max. std dev 66.......015884 Report the summary statistics in degree Celsius.

Given the relationship between Fahrenheit (F) and Celsius (C) temperatures, \( F = \frac{9}{5} C + 32 \), we can invert this equation to find Celsius in terms of Fahrenheit: \( C = \frac{5}{9} (F - 32) \). To report summary statistics in Celsius, each of the given Fahrenheit statistics needs to be converted using this formula.

Conversion Process

The summary statistics provided include minimum, first quartile (Q1), median, mean, third quartile (Q3), maximum, and standard deviation. Each of these will be individually converted from Fahrenheit to Celsius.

Converting the Summary Statistics

• Minimum (F = 66):

  C = (5/9) (66 - 32) = (5/9) 34 ≈ 18.89°C

• First Quartile (F = ...):

  Since the exact value is missing in the summary, the general approach is to apply C = (5/9)*(F - 32) to the given F statistic once provided.

• Median (F = ...):

  Similarly, apply C = (5/9)*(F - 32).

• Mean (F = ...):

  Same conversion applies, taking the mean Fahrenheit value and converting it to Celsius.

• Third Quartile (F = ...):

  Convert using the same formula.

• Maximum (F = ...):

  Apply C = (5/9)*(Max - 32).

• Standard Deviation (F = ...):

  Convert as follows: Since standard deviation in Fahrenheit measures spread, the conversion involves scaling by 5/9:

  σ_C = (5/9) * σ_F.

However, because the exact Fahrenheit values are not fully provided in the prompt (notably after the minimum of 66 and the subsequent statistical points), the specific numerical conversions cannot be completed precisely. Nonetheless, the methodology remains consistent: subtract 32 from each Fahrenheit statistic, then multiply by 5/9 to obtain Celsius equivalents. The standard deviation in Celsius can be derived by multiplying the Fahrenheit standard deviation by 5/9.

Interpreting the Converted Statistics

Once obtained, the Celsius summary statistics will allow for meaningful interpretation of temperature data in Celsius units. Typically, the median provides the central tendency, while the quartiles offer insights into the distribution spread. The minimum and maximum define the range, and the standard deviation describes variability. These transformed statistics are crucial for analyzing temperature patterns in a more globally standard unit, facilitating comparability across regions or datasets where Celsius is the preferred measurement scale.

Conclusion

In summary, transforming the temperature summary statistics from Fahrenheit to Celsius involves applying the formula \( C = (5/9) (F - 32) \) to all relevant statistics. Despite incomplete numerical data in the prompt, the methodology remains consistent: subtract 32 from each Fahrenheit value and multiply by 5/9. This process ensures that temperature data reported in Celsius accurately reflects the original Fahrenheit-based observations, supporting detailed analysis in scientific and practical contexts.

References

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