An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Use boxplot(gain ~ feed, data = data, main = "Weight Gain by Feed Type", xlab = "Feed Type", ylab = "Weight Gain (pounds)") to draw the boxplot.
Check the center (median) of each group.
Check the spread (IQR) of each group.
Check for outliers and symmetry.
Explanation
Problem Analysis The problem provides data on weight gain of pigs fed three different feeds (A, B, and C). The goal is to generate a side-by-side boxplot to visualize the distribution of weight gain for each feed type and to identify key features from the boxplot.
R Code for Boxplot The R code to generate the side-by-side boxplot is:
boxplot(gain ~ feed, data = data, main = "Weight Gain by Feed Type", xlab = "Feed Type", ylab = "Weight Gain (pounds)")
This code uses the boxplot() function in R. The formula gain ~ feed specifies that we want to create boxplots of 'gain' for each level of 'feed'. The data = data argument specifies the data frame containing the variables. The main , xlab , and ylab arguments add a title and labels to the plot.
Main Things to Check The main things to check from a side-by-side boxplot are:
Center (Median): The horizontal line inside each box represents the median weight gain for that feed type. Comparing the medians allows us to see which feed type tends to result in higher weight gain.
Spread (IQR): The box itself represents the interquartile range (IQR), which is the range between the 25th and 75th percentiles. The IQR indicates the variability of weight gain within each feed type. A larger box indicates greater variability.
Outliers: Points plotted outside the whiskers are considered outliers. Outliers represent unusually high or low weight gains for a particular feed type.
Symmetry: The position of the median within the box and the lengths of the whiskers can give an indication of the symmetry of the data. If the median is in the center of the box and the whiskers are of equal length, the data is approximately symmetric. If the median is closer to one end of the box or the whiskers are of different lengths, the data is skewed.
Range: The whiskers extend to the most extreme data point which is no more than 1.5 times the box size (IQR) from the box. This gives an idea about the range of the data.
Differences in Variability: Compare the sizes of the boxes (IQRs) to see if the variability in weight gain differs significantly between the feed types.
Examples
Boxplots are useful in comparing the performance of different treatments or interventions. For example, in a clinical trial, boxplots could be used to compare the effectiveness of different drugs in reducing blood pressure. The boxplot would show the distribution of blood pressure reductions for each drug, allowing researchers to quickly assess the median reduction, the variability in response, and the presence of outliers.
A device delivering a current of 15.0 A for 30 seconds allows approximately 2.81 x 10^21 electrons to flow through it. This is calculated using the total charge produced by the current and the charge of a single electron. The steps included calculating total charge using the formula Q = I × t and then using the charge of an electron to find the number of electrons.
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