Geology The table below shows the number of major...

Geology The table below shows the number of major earthquakes (magnitude 7.0 or greater) worldwide in the ten-year period from 1991 through 2000 . a. Find the mean and the median of the numbers of annual earthquakes. b. Do the data include an outlier that you should discard? Explain. c. Compare the box-and-whisker plots at the right. One shows the data above. The other shows worldwide earthquake data from 1900 through 2000 . What conclusions can you draw about recent earthquakes? Justify your reasoning.

Geology The table below shows the number of major earthquakes (magnitude 7.0 or greater) worldwide in the ten-year period from 1991 through 2000 .
a. Find the mean and the median of the numbers of annual earthquakes.
b. Do the data include an outlier that you should discard? Explain.
c. Compare the box-and-whisker plots at the right. One shows the data above. The other shows worldwide earthquake data from 1900 through 2000 . What conclusions can you draw about recent earthquakes? Justify your reasoning.

Key Concepts

Box-and-Whisker Plot

A box-and-whisker plot is a graphical representation of a data set that summarizes its distribution through five key statistics: the minimum, first quartile, median, third quartile, and maximum. It provides a visual depiction of the spread, central value, and variability of the data, and it can also highlight potential outliers.

Comparative Data Analysis

Comparative data analysis involves examining two or more data sets to identify similarities, differences, trends, or patterns over time or between groups. This approach helps in understanding changes in distribution, central tendencies, variability, and the impact of outliers, thereby enabling informed conclusions about shifts in the data over different periods.

Median

The median is another measure of central tendency, defined as the middle value in an ordered data set. When data is sorted from smallest to largest, the median gives a value such that half of the data points fall below it and the other half above it. Unlike the mean, the median is less affected by outliers, making it a robust indicator of central tendency in skewed distributions.

Mean

The mean is a measure of central tendency that represents the arithmetic average of a data set. It is calculated by adding all the values together and then dividing by the number of values. The mean is useful in understanding the overall level around which the data points cluster, though it can be sensitive to extreme values in the data set.

Outliers

Outliers are data points that significantly differ from the other observations in a sample. They can have a disproportionate influence on statistical measures like the mean, and their presence might indicate variability in the measurement, experimental error, or novel insights. Identifying and appropriately handling outliers is crucial for accurate data analysis.

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