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The MCQs below are drawn from the Statistics subject category.
Showing 1211–1220
of 1558 MCQs
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1211
Which theorem provides a method to determine the minimum proportion of observations that fall within a specific number of standard deviations from the mean for any distribution?
Chebyshev's Theorem states that for any data distribution, the proportion of observations falling within k standard deviations of the mean is at least 1 - (1/k²), where k > 1. This theorem is powerful because it applies to any distribution, regardless of its shape.
1212
What is the resulting value when the arithmetic mean is multiplied by the coefficient of variation?
The coefficient of variation (CV) is defined as the ratio of the standard deviation to the arithmetic mean (CV = σ / μ). Therefore, multiplying the arithmetic mean by the coefficient of variation yields the standard deviation (σ = CV * μ).
1213
Calculate the coefficient of variation for a distribution with a mean of 14 and a standard deviation of 5.
The coefficient of variation (CV) is calculated as (Standard Deviation / Mean) * 100. Here, (5 / 14) * 100 equals approximately 35.71%. This metric is a dimensionless measure of relative variability, allowing for the comparison of dispersion across different datasets regardless of their units.
1214
How are ratios derived from absolute variations in recorded observations typically classified in statistical analysis?
Relative measures of dispersion, such as the coefficient of variation, are dimensionless ratios that allow for the comparison of variability between different datasets, regardless of the units of measurement used for the original observations.
1215
Which statistical measure is commonly utilized to assess the consistency or relative variability of different datasets?
The Coefficient of Variation (CV) is a standardized measure of dispersion defined as the ratio of the standard deviation to the mean. It is widely used in statistics to compare the relative variability or consistency of two or more datasets, especially when the units of measurement differ or when the means of the datasets are significantly different, as it expresses the standard deviation as a percentage of the mean.
1216
What is another term for relative measures of dispersion?
Relative measures of dispersion are ratios that express the spread of data independently of the units of measurement. The coefficient of variation is the most common relative measure, calculated as the ratio of the standard deviation to the mean, often expressed as a percentage.
1217
Calculate the Coefficient of Variation (C.V.) if the mean is 25 and the standard deviation is 5.
The Coefficient of Variation is calculated using the formula C.V. = (Standard Deviation / Mean) * 100. Substituting the given values: (5 / 25) * 100 = 0.2 * 100 = 20%. This metric expresses the standard deviation as a percentage of the mean, allowing for comparison of variability between different datasets.
1218
Which statistician is credited with introducing the concepts of standard deviation and the coefficient of variation?
Karl Pearson is widely recognized for formalizing the concept of standard deviation as a measure of dispersion and introducing the coefficient of variation in the late 19th century. These contributions were fundamental in establishing modern descriptive statistics and comparative data analysis.
1219
If the arithmetic mean is 78 and the coefficient of variation is 12.3%, what is the standard deviation?
The coefficient of variation (CV) is calculated as (Standard Deviation / Mean) * 100. Given CV = 12.3% and Mean = 78, we rearrange the formula: Standard Deviation = (CV * Mean) / 100. Substituting the values: (12.3 * 78) / 100 = 959.4 / 100 = 9.594. This confirms the standard deviation is 9.594.
1220
Calculate the coefficient of variation (CV) for the dataset: 2, 4, 8, 6, 10, 12.
The coefficient of variation is calculated as (standard deviation / mean) * 100. For the data {2, 4, 8, 6, 10, 12}, the mean is 7 and the standard deviation is approximately 3.415. Thus, (3.415 / 7) * 100 equals approximately 48.79%, which rounds to 48.86% depending on the precision of the variance calculation used.
