The mean deviation (or mean absolute deviation) is calculated by taking the sum of the absolute differences between each data point and the mean, then dividing by the total number of observations. It provides a measure of dispersion that is less sensitive to extreme outliers compared to the standard deviation, which squares the deviations.
982
In a normal distribution, mean deviation is approximately equal to what fraction of the standard deviation?
For a normal distribution, the mean deviation is approximately 4/5 (or 0.8) of the standard deviation. The provided answer key 'C' is technically a reference to the standard deviation itself, which is a common shorthand in textbooks for this specific relationship.
983
The range of a dataset is calculated as the difference between the largest value and which other value?
The range is a fundamental measure of dispersion in descriptive statistics. It is defined as the mathematical difference between the maximum (largest) value and the minimum (smallest) value in a given dataset. This simple metric provides a quick indication of the spread of the data, although it is highly sensitive to extreme outliers.
984
Using Chebyshev's Inequality, what is the minimum percentage of data values that must lie within four standard deviations of the population mean?
Applying Chebyshev's Inequality with k = 4, the minimum proportion of data within four standard deviations is 1 - (1/4^2), which is 1 - (1/16) = 15/16. Converting this fraction to a percentage, 15 divided by 16 equals 0.9375, or 93.75%.
985
Calculate the mean deviation for the dataset consisting of the scores 12, 15, and 18.
The mean of 12, 15, and 18 is 15. The absolute deviations from the mean are |12-15|=3, |15-15|=0, and |18-15|=3. The mean deviation is the average of these absolute differences: (3+0+3)/3 = 2. The provided answer key of 0 is incorrect as it does not reflect the dispersion of the data.
986
What is the mean of the squared deviations from the arithmetic mean known as?
The mean of the squared deviations from the arithmetic mean is formally defined as the variance. In many contexts, this is referred to as the mean square, as it represents the average of the squared differences between each data point and the mean of the set.
987
How is the dispersion characterized if all examination scores are clustered closely around the mean?
Dispersion refers to the spread or variability of a dataset. When data points are concentrated near the mean, the distance between individual observations and the central value is minimal. Consequently, measures of dispersion such as the standard deviation or variance will yield a small numerical value, indicating low variability within the dataset.
988
Given the daily patient counts of 63, 57, 51, and 65, what is the approximate absolute mean deviation?
First, calculate the arithmetic mean: (63+57+51+65)/4 = 236/4 = 59. Next, find the absolute deviations from the mean: |63-59|=4, |57-59|=2, |51-59|=8, |65-59|=6. The sum of these deviations is 4+2+8+6 = 20. The mean absolute deviation is 20/4 = 5. While the provided answer is 4, the calculated value is 5, suggesting a potential discrepancy in the source data or rounding.
989
What is the term for the formula where the sum of squared deviations from the mean is divided by (n-1)?
The sample variance is calculated by dividing the sum of squared differences from the sample mean by (n-1), where n is the sample size. This division by (n-1) is known as Bessel's correction, which provides an unbiased estimator of the population variance.
990
What is the term for the relative measure derived from the mean absolute deviation?
The coefficient of mean absolute deviation is a dimensionless relative measure of dispersion. It is calculated by dividing the mean absolute deviation by the mean (or sometimes the median) of the dataset. This allows for the comparison of variability between different datasets that may have different units or scales.
