Select the correct answer from each drop-down menu.
Brittany surveyed the students in three different Chemistry classes regarding the average number of hours of sleep they get each night. She calculated the mean and standard deviation, SD, of the data and recorded the results in the table below.
| Class A | Class B | Class C |
| :-------- | :-------- | :-------- |
| Mean=7.35 | Mean=6.87 | Mean=8.14 |
| SD=2.92 | SD=3.65 | SD =3.10 |
Use the information provided to complete the following statement.
Class $\square$ shows the most consistency in the number of hours slept per night because the $\square$ is the $\square$.
Answer (2)
The problem provides the standard deviations of sleep hours for three classes.
The class with the smallest standard deviation is the most consistent.
Comparing the standard deviations, Class A has the smallest SD of 2.92.
Therefore, Class A shows the most consistency because its standard deviation is the smallest .
Explanation
Analyze the problem We are given the mean and standard deviation of the number of hours slept per night for three different Chemistry classes. We need to determine which class shows the most consistency in the number of hours slept per night. The class with the smallest standard deviation is the most consistent.
Compare standard deviations The standard deviations for the three classes are: Class A: SD = 2.92 Class B: SD = 3.65 Class C: SD = 3.10 Comparing these values, we see that the smallest standard deviation is 2.92, which corresponds to Class A.
Determine the most consistent class Therefore, Class A shows the most consistency in the number of hours slept per night because the standard deviation is the smallest.
State the final answer The final answer is Class A, standard deviation, smallest.
Examples
Understanding consistency in data is crucial in many real-world scenarios. For example, in manufacturing, a company wants to ensure that the products they produce are consistent in quality. By measuring a certain characteristic of the product and calculating the standard deviation, they can determine how consistent the production process is. A smaller standard deviation indicates higher consistency, meaning the products are more uniform in quality. This helps maintain customer satisfaction and reduces waste due to defective products.
Class A shows the most consistency in the number of hours slept per night because it has the smallest standard deviation of 2.92. Comparing the standard deviations, Class B and Class C have larger values, indicating more variability. Therefore, Class A is the most consistent.
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