Question: The arithmetic mean of five daily temperature readings for birds is 22°C. If four readings are 20, 21, 23, and 24, what is the fifth?
["Understanding the Arithmetic Mean: Solving a Birdwatching Temperature Puzzle", "When observing birds, temperature plays a crucial role in understanding their behavior, habitat conditions, and migration patterns. A common mathematical method used in environmental science is calculating the arithmetic mean—a simple yet powerful tool to summarize daily temperature data.", "In this article, we explore a practical problem rooted in birdwatching: determining the missing daily temperature when the arithmetic mean of five readings is known.", "---", "### The Problem Statement", "Suppose five daily temperature readings affect bird activity, and scientists observe that the arithmetic mean is 22°C. Four of the temperature values are recorded: 20°C, 21°C, 23°C, and 24°C. The challenge is to find the fifth temperature.", "---", "### What Is the Arithmetic Mean?", "The arithmetic mean measures the average of a set of numbers. It is calculated by summing all values and dividing by the number of values.", "Mathematically, for five temperatures ( T_1, T_2, T_3, T_4, T_5 ):", "[\n\ ext{Mean} = \frac{T_1 + T_2 + T_3 + T_4 + T_5}{5}\n]", "---", "### Given Data", "- Mean = 22°C\n- Known temperatures: 20, 21, 23, 24\n- Let the unknown fifth temperature be ( x )", "---", "### Setting Up the Equation", "Using the formula for the arithmetic mean:", "[\n\frac{20 + 21 + 23 + 24 + x}{5} = 22\n]", "First, sum the known temperatures:", "[\n20 + 21 + 23 + 24 = 88\n]", "So the equation becomes:", "[\n\frac{88 + x}{5} = 22\n]", "---", "### Solving for ( x )", "Multiply both sides by 5:", "[\n88 + x = 110\n]", "Subtract 88 from both sides:", "[\nx = 110 - 88 = 22\n]", "---", "### Final Answer", "The fifth daily temperature reading is 22°C.", "---", "### Why This Matters in Bird Research", "Temperature averages help ornithologists track climate impacts on bird populations. Knowing precise averages supports conservation efforts, habitat modeling, and behavior studies. This kind of math—simple yet essential—enables birdwatchers and scientists to interpret environmental data effectively.", "---", "Key Takeaways:", "- The arithmetic mean provides a reliable average from daily temperature readings.\n- Missing temperature values can be found using the mean formula efficiently.\n- Accurate temperature data supports broader ecological research and bird conservation.", "---", "Whether you’re a casual birdwatcher or an aspiring ecologist, mastering basic statistics enhances your ability to understand nature’s patterns through numbers. If the average of five daily temperatures is 22°C and four readings are 20, 21, 23, and 24, the missing fifth temperature is 22°C."]
