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What is the arithmetic mean of the absolute values of the deviations of the individual values from the mean in a data set?

It is the mean absolute deviation.


Why don't we measure spread about the mean by simply averaging the deviations of individual data values from their mean?

Averaging the deviations of individual data values from their mean would always result in zero, since the mean is the point at which the sum of deviations is balanced. This occurs because positive and negative deviations cancel each other out. Instead, measures like variance and standard deviation are used, which square the deviations to ensure all values contribute positively, providing a meaningful representation of spread around the mean.


How many standard deviations a measurement is away from the mean?

The answer depends on the individual measurement in question as well as the mean and standard deviation of the data set.


In a standard normal distribution 95 percent of the data is within plus standard deviations of the mean?

95% is within 2 standard deviations of the mean.


When a data set is normally distributed about how much of the data fall within two standard deviations of the mean?

In a normally distributed data set, approximately 95% of the data falls within two standard deviations of the mean. This is part of the empirical rule, which states that about 68% of the data falls within one standard deviation and about 99.7% falls within three standard deviations. Therefore, two standard deviations capture a significant majority of the data points.


What is the mean absolute deviation of the data set shown?

To calculate the mean absolute deviation (MAD) of a data set, first find the mean of the data. Then, subtract the mean from each data point to find the absolute deviations. Finally, take the average of these absolute deviations. If you provide the specific data set, I can help calculate the MAD for you.


What is the standard deviation?

The standard deviation of a set of data is a measure of the spread of the observations. It is the square root of the mean squared deviations from the mean of the data.


What percentage of data would fall within 1.75 standard deviations of the mean?

About 81.5%


What is a coded-deviation method in statistics?

Differing from standard deviations, the coded deviation method finds the mean of grouped data from the assumed mean using unit deviations. This is a shorter way to find the mean.


Is variance based on deviations from the mean?

Variance is the squared deviation from the mean. (X bar - X data)^2


What does standard deviation help you find?

Standard deviation helps you identify the relative level of variation from the mean or equation approximating the relationship in the data set. In a normal distribution 1 standard deviation left or right of the mean = 68.2% of the data 2 standard deviations left or right of the mean = 95.4% of the data 3 standard deviations left or right of the mean = 99.6% of the data


In a normal distribution what percentage of the data falls within 2 standard deviation of the mean?

In a normal distribution, approximately 95% of the data falls within 2 standard deviations of the mean. This is part of the empirical rule, which states that about 68% of the data is within 1 standard deviation, and about 99.7% is within 3 standard deviations. Therefore, the range within 2 standard deviations captures a significant majority of the data points.

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