An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
An electric device with a current of 15.0 A for 30 seconds causes approximately 2.81 x 10^21 electrons to flow through it. This calculation involves determining the total charge using the formula Q = I ⋅ t , and then converting that charge into the number of electrons using the charge of a single electron. Thus, the answer is that roughly 2.81 x 10^21 electrons flow through the device.
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Create a frequency distribution table.
Calculate the mode: 26.
Calculate the mean: 34.74.
Calculate the median: 34.0.
Calculate the variance: 86.033.
Calculate the standard deviation: 9.275.
Mode = 26 , Mean = 34.74 , Median = 34.0 , Variance = 86.033 , Standard Deviation = 9.275
Explanation
Analyze the problem We are given a dataset of 50 numbers and asked to perform several statistical analyses: create a frequency distribution table, calculate the mode, mean, and median, and calculate the variance and standard deviation.
Create frequency distribution table First, we create the frequency distribution table using the specified intervals. We count how many data points fall into each interval:
21-25: 8
26-30: 11
31-35: 9
36-40: 8
41-45: 6
46-50: 7
51-55: 0
56-60: 1
Calculate the mode Next, we calculate the mode, which is the value that appears most frequently in the dataset. From the calculations, the mode is 26.
Calculate the mean Now, we calculate the mean, which is the average of all the data points. The mean is calculated as: Mean = Number of data points Sum of all data points = n ∑ x i The calculated mean is 34.74.
Calculate the median We then calculate the median, which is the middle value of the sorted dataset. Since we have 50 data points (an even number), the median is the average of the 25th and 26th values when the data is sorted. The calculated median is 34.0.
Calculate the variance Next, we calculate the variance, which measures the spread of the data around the mean. The formula for the sample variance is: Variance = n − 1 ∑ ( x i − mean ) 2 The calculated variance is 86.033.
Calculate the standard deviation Finally, we calculate the standard deviation, which is the square root of the variance. The standard deviation is: Standard Deviation = Variance The calculated standard deviation is 9.275.
State the final answer The frequency distribution table is:
21-25: 8
26-30: 11
31-35: 9
36-40: 8
41-45: 6
46-50: 7
51-55: 0
56-60: 1
The mode is 26, the mean is 34.74, the median is 34.0, the variance is 86.033, and the standard deviation is 9.275.
Examples
Understanding the distribution and spread of data is crucial in many real-world scenarios. For example, in quality control, a manufacturer might analyze the lengths of produced parts. The mean length indicates the average size, the variance indicates the consistency of the production process, and the frequency distribution helps identify common size ranges. This information helps the manufacturer ensure that the parts meet the required specifications and identify any potential issues in the production line. Similarly, in finance, analyzing the mean and standard deviation of stock returns helps investors assess the risk and potential reward of different investments. A higher standard deviation indicates higher volatility and thus higher risk.
