To accurately identify the various components of a box-and-whiskers plot such as lower extrema, upper extrema, median, lower quartile, upper quartile, range, and interquartile range, I would need you to provide some specific numerical data or a visual representation of the box-and-whiskers plot.
However, I can explain how to find each of these components if you have the data.
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Lower Extrema: This is the smallest data point in the dataset (or the minimum value) that is not considered an outlier.
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Upper Extrema: This is the largest data point in the dataset (or the maximum value) that is not considered an outlier.
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Median: This is the middle value of the dataset when it is ordered from smallest to largest. If there is an even number of values, the median is the average of the two middle values.
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Lower Quartile (Q1): This is the median of the lower half of the dataset (the first 25% of the data).
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Upper Quartile (Q3): This is the median of the upper half of the dataset (the first 75% of the data).
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Range: This is the difference between the upper extrema and the lower extrema. \[ \text{Range} = \text{Upper Extrema} - \text{Lower Extrema} \]
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Interquartile Range (IQR): This measures the spread of the middle 50% of the data and is calculated as: \[ \text{IQR} = Q3 - Q1 \]
If you provide the data points or characteristics of the box-and-whiskers plot, I could help you identify these components specifically.
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