Question

The record January temperatures (in degrees Fahrenheit) for a city are given. Find the distance between the numbers to determine the range of temperatures for January.Flagstaff, Arizona: lowest: \(-22^{\circ} \mathrm{F}\) highest: \(66^{\circ} \mathrm{F}\)

Short answer

The range of January temperatures in Flagstaff, Arizona is \(88^{\circ} \mathrm{F}\).

Step-by-step solution

Identify High and Low Temperatures

The highest recorded temperature for January in Flagstaff, Arizona is \(66^{\circ} \mathrm{F}\), and the lowest is \(-22^{\circ} \mathrm{F}\).

Calculate the Range

The range of the temperatures can be calculated by subtracting the lowest temperature from the highest. So, the range is \(66^{\circ} \mathrm{F}\) - \((-22)^{\circ} \mathrm{F}\).

Simplify the Result

By performing the subtraction in Step 2, we get a result of \(88^{\circ} \mathrm{F}\). This is the range of temperatures for January.

Key concepts

Temperature Range Calculation

Understanding how to calculate the temperature range is crucial for students studying meteorology, geography, or any field dealing with climatic data. In essence, this calculation provides us with a simple measure of the variability in temperature over a set period. The temperature range is determined by subtracting the lowest recorded temperature from the highest.

In the example of Flagstaff, Arizona, the process is straightforward: we start with the highest recorded temperature, which is given as \(66^{\text{\textdegree}}F\), and from this, we subtract the lowest recorded temperature, \(\text{-}22^{\text{\textdegree}}F\). When performing this subtraction, we add the two numbers since the lower temperature is negative. This results in a range of \(88^{\text{\textdegree}}F\).

Remember to take care when dealing with negative numbers in this calculation. Since temperature differences are absolute values, a negative sign indicates that the value is below some reference point, such as freezing point, but does not affect the numerical difference when calculating ranges. A larger temperature range could indicate a location with dramatic temperature shifts, which might have implications for things like heating costs, wardrobe choices, or even crop viability.

Temperature in Degrees Fahrenheit

Understanding the Fahrenheit scale is key for solving problems involving temperatures in the United States, where this unit is commonly used. Degrees Fahrenheit (°F) is a temperature scale where the freezing point of water is 32°F and the boiling point is 212°F under standard atmospheric conditions.

To convert temperatures from Celsius to Fahrenheit, one can use the formula: \(°F = °C \times \frac{9}{5} + 32\). Conversely, to convert from Fahrenheit to Celsius, the equation is: \(°C = (°F - 32) \times \frac{5}{9}\). It's necessary to understand the Fahrenheit scale to accurately interpret temperature readings and perform calculations like our temperature range determination.

Statistical Range

The statistical range is not only applicable in weather temperature analysis but is an important concept across various scientific and statistical studies. It represents the difference between the highest and lowest values within a set of data, thus providing a basic measure of the spread or dispersion of the data set.

A broader range indicates a larger disparity between data points, while a narrower range suggests that the data points are closer in value to each other. It is a primary step in data analysis and helps to understand the variability of a particular dataset before diving into more complex statistical measures like the mean, median, standard deviation, and quartiles.

When interpreting ranges, one should also consider the context of the data. For instance, a wide temperature range for a specific day may indicate a sharp change in weather conditions, which could be critical information for event planning or agriculture. Consequently, mastering the concept of statistical range is essential for students and professionals dealing with any form of data analysis.