An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Calculate the mean of each row: Row 1 is 7, Row 2 is 6, Row 3 is 10, Row 4 is 6.5.
Identify the row with the largest mean: Row 3.
Identify the row with the smallest mean: Row 2.
Determine the range within which the actual population mean lies: between 1 and 20.
The largest mean is Row 3, the smallest mean is Row 2, and the actual population mean will be between 1 and 20 .
Explanation
Analyze the problem and data We are given a table of population data with 4 rows and 4 columns. Serena selects 4 samples from the table, which means she selects all the numbers in a row. We need to determine which row will give her the largest mean, which row will give her the smallest mean, and the range within which the actual population mean will lie.
Calculate row means First, we calculate the mean of each row by summing the numbers in the row and dividing by 4.
Detailed row mean calculations The means of the rows are calculated as follows:
Row 1: 4 4 + 8 + 6 + 10 = 4 28 = 7 Row 2: 4 5 + 2 + 9 + 8 = 4 24 = 6 Row 3: 4 9 + 20 + 10 + 1 = 4 40 = 10 Row 4: 4 15 + 1 + 8 + 2 = 4 26 = 6.5
Identify largest and smallest row means From the row means calculated above, we can see that:
The largest mean is 10, which corresponds to Row 3.
The smallest mean is 6, which corresponds to Row 2.
Calculate population mean Next, we calculate the overall population mean by summing all the numbers in the table and dividing by 16.
Detailed population mean calculation The sum of all numbers in the table is: 4 + 8 + 6 + 10 + 5 + 2 + 9 + 8 + 9 + 20 + 10 + 1 + 15 + 1 + 8 + 2 = 118 The overall population mean is: 16 118 = 7.375
Determine the range for the population mean The minimum value in the table is 1, and the maximum value is 20. Therefore, the actual population mean will be between 1 and 20.
State the final answer Therefore, the row with the largest mean is Row 3, the row with the smallest mean is Row 2, and the actual population mean will be between 1 and 20.
Examples
Understanding means is crucial in many real-world scenarios. For instance, if you're analyzing sales data for different product lines, calculating the average sales per product line helps you identify which products are performing best. Similarly, in environmental science, you might calculate the average pollutant levels in different areas to pinpoint pollution hotspots. These averages provide a clear, concise way to compare different datasets and make informed decisions.
A current of 15.0 A for 30 seconds results in a total charge of 450 C . This corresponds to approximately 2.81 × 1 0 21 electrons flowing through the device.
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