Question

a researcher studied the relationship between the number of times a certain species of cricket will chirp in one minute and the temperature outside. her data is expressed in the scatter plot and line of best fit below. what does the point (134, 75.6) represent?
answer
an expected temperature of 134°f when the cricket has chirped 75.6 times.
actual temperature of 134°f when the cricket has chirped 75.6 times.
actual temperature of 75.6°f when the cricket has chirped 134 times.
an expected temperature of 75.6°f when the cricket has chirped 134 times.

Explanation:

The x - axis of the scatter plot represents the number of chirps per minute and the y - axis represents the temperature in degrees Fahrenheit. The line of best fit is used to predict values. The point \((134, 75.6)\) on the line of best fit means that when the cricket chirps 134 times per minute, the expected temperature (based on the line of best fit) is \(75.6^{\circ}\text{F}\). We analyze each option:

• Option 1: Says "An expected temperature of \(134^{\circ}\text{F}\) when the cricket has chirped 75.6 times" - this swaps the x and y values, so it's incorrect.
• Option 2: Says "Actual temperature of \(75.6^{\circ}\text{F}\) when the cricket has chirped 134 times" - the line of best fit gives expected (predicted) values, not actual values from the data points (the actual data points are around the line), so this is incorrect.
• Option 3: Says "Actual temperature of \(134^{\circ}\text{F}\) when the cricket has chirped 75.6 times" - swaps x and y and misinterprets actual vs expected, incorrect.
• Option 4: Says "An expected temperature of \(75.6^{\circ}\text{F}\) when the cricket has chirped 134 times" - this correctly interprets the x (chirps = 134) and y (temperature = 75.6) values of the point on the line of best fit as a predicted (expected) temperature for 134 chirps.

Answer:

An expected temperature of \(75.6^{\circ}\text{F}\) when the cricket has chirped 134 times. (The option corresponding to this description, likely the fourth option in the original multiple - choice setup)