Statistics Chapter 5 Quiz

Coefficient of Variation Interpretation

• The coefficient of variation (CV) for datasets X and Y indicates the relative variability or dispersion of the data sets, expressed as a percentage of the mean. A higher CV suggests greater variability relative to the mean.

Robustness of Dispersion Measures

• The interquartile range (IQR) is considered a more robust measure of dispersion than the standard deviation or range because it is less sensitive to outliers.

70th Percentile Calculation

• The 70th percentile for the dataset X = {1,2,3,4,5,6,6,8,9,10} is 7. This is calculated by finding the value that is greater than 70% of the data points when the data set is ordered from least to greatest.

Standard Deviation Calculation

• For the dataset X = {1,2,2,3}, the standard deviation is approximately 0.82.

65th Percentile Calculation Method

• The 65th percentile of X = {1,2,3,4,5,6,6,8,9,10} is calculated by first ordering the data, then identifying the value that is greater than 65% of the data points. Linear interpolation between values may be needed to determine the exact percentile.

Purpose of a Sample in Statistics

• The primary purpose of a sample in statistics is to make inferences about a larger population based on a smaller, manageable subset.

Measure of Centrality: Median

• The median is the measure of centrality defined as the middle value when the dataset is ordered.

Variance in a Uniform Dataset

• In a dataset where all values are the same, the variance is zero.

Mean Absolute Deviation (MAD)

• The mean absolute deviation (MAD) is the measure of dispersion defined as the average distance of each data point from the mean.

Mode Preference

• The mode is preferred over the mean and median when dealing with categorical or discrete data, or when the data is strongly skewed. The mode is also useful when the data has multiple peaks.

Bimodal Dataset Example

• A bimodal dataset is one that has two distinct peaks or modes in its distribution which will be indicated in a histogram.

Limitations of Range as a Measure of Dispersion

• A limitation of the range as a measure of dispersion is its extreme sensitivity to outliers; a single outlier can drastically affect the range.

Variance Formula Interpretation

• The expression Var(X) = E[(x - mean)²] represents the variance of a random variable X, calculated as the expected value of the squared differences between each data point (x) and the mean.