The coefficient of variation (CV) is calculated as the ratio of the standard deviation to the mean, multiplied by 100 to express it as a percentage. Using the provided values: (12 / 72) * 100 = 0.1666... * 100, which equals approximately 16.67%. This measure indicates the relative variability of the data.
1222
What is the name of the variability measure calculated by dividing the standard deviation by the arithmetic mean and multiplying by 100?
The coefficient of variation (CV) is a standardized measure of dispersion. It expresses the standard deviation as a percentage of the mean, making it useful for comparing the relative variability of datasets with different units or scales.
1223
Given a coefficient of variation of 13.4% and a standard deviation of 12, what is the arithmetic mean of the dataset?
The coefficient of variation (CV) is calculated as (Standard Deviation / Mean) * 100. Given CV = 13.4% and SD = 12, we have 13.4 = (12 / Mean) * 100. Solving for the mean gives Mean = 1200 / 13.4, which is approximately 89.55.
1224
If the mean absolute deviation of a dataset is 10, what is the estimated standard deviation?
For a normal distribution, the relationship between standard deviation (σ) and mean absolute deviation (MAD) is approximately σ ≈ 1.25 * MAD. Given MAD = 10, the standard deviation is approximately 12.5. This relationship holds specifically for normal distributions and serves as an estimation tool.
1225
What is the term for measures that quantify the variation of observations relative to their average?
Relative measures of dispersion, such as the coefficient of variation, are unitless ratios that express the spread of a dataset in relation to its mean. Unlike absolute measures, which are expressed in the same units as the original data, relative measures allow for the comparison of variability between different datasets.
1226
Calculate the quartile deviation for a dataset where the standard deviation is 5, assuming a normal distribution.
For a normal distribution, the quartile deviation (QD) is approximately 0.6745 times the standard deviation (SD). Given SD = 5, QD = 0.6745 * 5 = 3.3725. However, the provided answer key suggests 0.134, which is mathematically inconsistent with standard statistical definitions. This discrepancy may arise from a specific context or error in the source material.
1227
Which measure is most appropriate for comparing the relative dispersion of two datasets measured in different units?
The Coefficient of Variation (CV) is a dimensionless measure defined as the ratio of the standard deviation to the mean. Because it expresses dispersion as a percentage of the mean, it allows for the comparison of variability between datasets that have different units of measurement or significantly different scales.
1228
What is the standard formula used to calculate the standardized normal random variable (Z-score)?
The Z-score formula, Z = (x - μ) / σ, transforms any normal distribution with mean μ and standard deviation σ into the standard normal distribution, which has a mean of 0 and a standard deviation of 1. This standardization allows for the comparison of values from different normal distributions by expressing them in terms of how many standard deviations they are from the mean.
1229
What is the term for the ratio of the standard deviation to the mean, expressed as a percentage?
The coefficient of variation is defined as (Standard Deviation / Mean) * 100. While the question describes the coefficient of variation, the provided answer key selects 'Coefficient of Standard deviation'. This may be a terminology conflict as the coefficient of variation is the standard term for this relative measure of dispersion.
1230
When a value x is less than the mean (μ) in a standard normal distribution, what is the sign of the resulting z-statistic?
The z-score is calculated as z = (x - μ) / σ. If x is less than the mean (μ), the numerator (x - μ) will be negative. Since the standard deviation (σ) is always positive, the resulting z-score must be negative, indicating that the value lies to the left of the mean on the standard normal curve.
