An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
A current of 15.0 A for 30 seconds results in a total charge of 450 C. Dividing this by the charge of a single electron (1.6 x 10^{-19} C) gives approximately 2.81 x 10^{21} electrons flowing through the device. Therefore, about 2.81 trillion trillion electrons pass through the device in 30 seconds.
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Calculate the first quartile (Q1) and third quartile (Q3): Q 1 = 70.5 , Q 3 = 88.0 .
Calculate the interquartile range (IQR): I QR = Q 3 − Q 1 = 17.5 .
Determine the lower and upper bounds: L o w er B o u n d = 44.25 , U pp er B o u n d = 114.25 .
Identify the outlier: 36 is less than the lower bound, so the outlier is 36 .
Explanation
Understanding the Problem We are given a dataset of homework scores and need to determine if there are any outliers. Outliers are data points that fall significantly outside the range of the other data points. We will use the interquartile range (IQR) method to identify potential outliers.
Calculating Quartiles First, we need to calculate the first quartile (Q1) and the third quartile (Q3) of the data. From the calculation tool, we have:
Q1 = 70.5 Q3 = 88.0
Calculating IQR Next, we calculate the interquartile range (IQR), which is the difference between Q3 and Q1:
I QR = Q 3 − Q 1 = 88.0 − 70.5 = 17.5
Determining Outlier Bounds Now, we determine the lower and upper bounds for outliers. Data points below the lower bound or above the upper bound will be considered outliers.
Lower Bound = Q1 - 1.5 * IQR = 70.5 - 1.5 * 17.5 = 70.5 - 26.25 = 44.25
Upper Bound = Q3 + 1.5 * IQR = 88.0 + 1.5 * 17.5 = 88.0 + 26.25 = 114.25
Identifying Outliers Finally, we identify any data points that fall outside the calculated bounds. Looking at the dataset, we see that the score 36 is less than the lower bound of 44.25. There are no scores greater than the upper bound of 114.25. Therefore, 36 is an outlier.
Conclusion Based on our calculations, the outlier in the dataset is 36.
Examples
Identifying outliers is crucial in many real-world scenarios. For instance, in quality control, detecting outliers can help identify defective products. In finance, it can flag fraudulent transactions. In education, like in this problem, it can highlight students who may need additional support or those who are exceptionally advanced. By understanding and addressing outliers, we can make more informed decisions and improve overall outcomes.
