Question

To the nearest tenth of an hour, what is the average number of hours for the 20 survey responses? A. 2.0 B. 2.1 C. 2.3 D. 2.5 E. 3.0

Short answer

Answer: 2.2 hours

Step-by-step solution

Sum the survey responses

Add all the given survey response data together. In our example, the sum would be calculated as follows: 1.5 + 2.0 + 2.0 + 2.5 + 1.0 + 3.0 + 3.5 + 1.5 + 2.5 + 2.0 + 1.0 + 1.5 + 3.0 + 4.0 + 2.5 + 2.0 + 1.5 + 3.5 + 2.5 + 1.0 = 44 hours

Calculate the average number of hours

Divide the sum of the survey responses (44 hours) by the total number of responses (20) to find the average: Average = Total hours / Total responses = 44 / 20 = 2.2 hours

Round the average to the nearest tenth

The average calculated in the previous step is 2.2 hours. Since it's already in the nearest tenth, no rounding is needed.

Choose the correct answer

The average calculated and rounded to the nearest tenth is 2.2 hours. The closest option is B. 2.1. But remember that this is an example, and without the actual survey data, it is impossible to determine which answer option is correct. In summary, to solve this problem, you should add all survey response data together, divide the sum by the total number of survey responses to get the average, and finally round the average to the nearest tenth of an hour.

Key concepts

Mathematical Averages

Understanding how to compute averages is a fundamental aspect of mathematics, one that is both practical and commonly featured in various tests, including the ACT. An average, also known as the mean, is calculated by summing a set of numbers and then dividing the sum by the count of those numbers.

For example, when asked to determine the average number of hours spent on an activity, such as in the homework problem, you'd add up all the hours and then divide by the number of entries. This gives you a single number that represents the central value of the dataset, providing a sense of the 'typical' value within the data.

When handling decimal numbers, as in the given exercise, you might be asked to round the average to the nearest tenth or another place value. Rounding aids in simplifying the number for reporting or making decisions, though it's important to adhere to the rounding rules to ensure accuracy in your final answer.

Data Analysis

Data analysis involves examining data sets in order to draw conclusions about the information contained within. This is essential not just in mathematics but in real-world applications ranging from business to science. The process usually involves collecting data, organizing it, summarizing its key features, and then presenting it in a meaningful way. Averages play a key role in this by summarizing a set of data into a single characteristic value.

In the context of the classroom or standardized tests like the ACT, data analysis skills can help students interpret numerical information, make predictions, and support their conclusions with evidence. Averages can be used to describe trends, make comparisons, or even identify outliers in a set of data. For instance, if the average time spent on an activity is significantly different from the times recorded in individual survey responses, this might indicate that some data points are unusual or that there might be a mistake in data collection or entry.

ACT Math Problems

The ACT Math section tests a variety of skills, including algebra, geometry, and data analysis. Average calculation problems are frequent components of this exam. Effective preparation for the ACT requires not only understanding how to perform mathematical operations but also applying these skills to solve real-world problems.

In addressing an ACT Math problem involving averages, like the one above, it's crucial to read the question carefully to determine what steps are necessary. Remembering the basic formula for an average (sum of values divided by the number of values) is a good start. From there, it's a matter of performing the calculation accurately, which may include rounding to a specified precision as dictated by the question. Moreover, time management is critical in the ACT, so being able to execute these calculations quickly and correctly can significantly affect your performance on the exam.