Josie Recorded The Average Monthly Temperatures For Two Citi
Josie Recorded The Average Monthly Temperatures For Two Cities In The
Josie recorded the average monthly temperatures for two cities in her state. For City 1, we are asked to find the mean (average) of the monthly temperatures and the mean absolute deviation of these temperatures, rounding to the nearest tenth. We are given the temperatures for City 1 as follows: 33°F, 79°F, 57°F, 32°F, 76°F, 36°F, 63°F, 80°F, 79°F, 61°F, 34°F, and 78°F.
Similarly, for City 2, although not directly asked in this particular problem, the temperatures are: 18°F, 64°F, 42°F, 17°F, 61°F, 21°F, 48°F, 65°F, 64°F, 46°F, 19°F, and 63°F. These figures serve as context or comparison but are not needed to solve the specific questions about City 1.
Paper For Above instruction
The problem requests to calculate the mean and the mean absolute deviation of the average monthly temperatures for City 1, based on the data provided. These statistical measures help us understand the central tendency and variability in the temperature data.
Calculating the Mean Temperature for City 1
The mean (average) is calculated by summing all the data points and dividing by the number of data points. For City 1, the monthly temperatures are 33°F, 79°F, 57°F, 32°F, 76°F, 36°F, 63°F, 80°F, 79°F, 61°F, 34°F, and 78°F. First, we sum all these values:
- 33 + 79 + 57 + 32 + 76 + 36 + 63 + 80 + 79 + 61 + 34 + 78 = 738
There are 12 months of data, so we divide the total sum by 12 to find the mean:
Mean = 738 ÷ 12 ≈ 61.5°F
Calculating the Mean Absolute Deviation (MAD)
The Mean Absolute Deviation measures the average distance of each data point from the mean, providing insight into the variability of the data set. To compute MAD for City 1, the steps involve:
- Calculate the absolute deviation of each temperature from the mean:
| Temperature | Absolute Deviation from Mean |
|---|---|
| 33°F | |33 - 61.5| = 28.5 |
| 79°F | |79 - 61.5| = 17.5 |
| 57°F | |57 - 61.5| = 4.5 |
| 32°F | |32 - 61.5| = 29.5 |
| 76°F | |76 - 61.5| = 14.5 |
| 36°F | |36 - 61.5| = 25.5 |
| 63°F | |63 - 61.5| = 1.5 |
| 80°F | |80 - 61.5| = 18.5 |
| 79°F | |79 - 61.5| = 17.5 |
| 61°F | |61 - 61.5| = 0.5 |
| 34°F | |34 - 61.5| = 27.5 |
| 78°F | |78 - 61.5| = 16.5 |
Next, sum all the absolute deviations:
- 28.5 + 17.5 + 4.5 + 29.5 + 14.5 + 25.5 + 1.5 + 18.5 + 17.5 + 0.5 + 27.5 + 16.5 = 182.0
Finally, divide this sum by 12 to find the MAD:
MAD = 182.0 ÷ 12 ≈ 15.2°F
Summary of Results
For City 1:
- The mean temperature is approximately 61.5°F.
- The mean absolute deviation is approximately 15.2°F.
These figures reflect the central tendency and variability of the temperature data, indicating that, on average, the monthly temperatures hover around 61.5°F with a typical deviation of about 15.2°F from the mean.
Conclusion
In analyzing the temperature data for City 1, calculating the mean provides insight into the typical temperature, while the MAD reveals the extent of fluctuation month-to-month. These statistical measures are vital for understanding climate patterns and planning purposes, such as agriculture, infrastructure, and energy consumption.
References
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