Measures of Central Tendency and Dispersion 3

A measure used to quantify the dispersion or diversity in nominal-level data. A higher IQV indicates more variability/diversity, and a lower IQV suggests greater similarity in the data.

IQV = 2 * (Total Possible Value - Sum of squared percentages) / (Total Possible Value per observation type) * (number of categories)

0.109 means that the 1996 frequency distribution of data shows 10.9% maximum variation.

0.144. The 2006 frequency distribution of data shows 14.4% maximum variation.

0.185. The 2016 frequency distribution shows 18.5% maximum variation.

Categorical variables (like ethnicity) without inherent order.

Data showing greater dispersion (more varied).

Data showing less dispersion (more similar or clustered).

The difference between the third quartile (Q3) and the first quartile (Q1) in a dataset.

The median of the lower half of a dataset after ordering the data.

The median of the upper half of a dataset after ordering the data.

The middle value in an ordered dataset.

Data arranged in ascending or descending order.

To find the difference between Q3 and Q1.

The part of data below the median.

The part of data above the median.

A measure of how spread out the data points are in a sample. It's calculated similarly to population standard deviation but uses n-1 in the denominator.

A measure of how spread out the data points are in an entire population. It's calculated using the formula with 'N' in the denominator.

The main difference lies in the denominator. Sample standard deviation uses 'n-1' to account for the fact that the sample is representing a larger population, while population standard deviation uses 'N' (the total number of individuals in the population).

Using (n-1) in the denominator for sample standard deviation creates an unbiased estimator of the population standard deviation. This means that the sample standard deviation is a better approximation of the true population standard deviation.

As the sample size increases, the difference between using n and n-1 in the denominator becomes smaller. For smaller samples, the difference can be significant.

A score that falls significantly outside the typical range of scores in a dataset.

The lowest acceptable score that's not considered unusually low.

The highest acceptable score that's not considered unusually high.

The average of a set of numbers, calculated by summing all values and dividing by the count.

A graph that displays the five-number summary of a dataset: minimum, first quartile, median, third quartile, and maximum.

A measure of how spread out the data is from the mean. It represents the average distance each data point is from the mean.

A relative measure of dispersion that compares the standard deviation to the mean, allowing for comparisons between variables with different scales.

A measure that describes dispersion in the original units of the variable (e.g., years, kilograms).

A measure that describes dispersion in a standardized way, allowing for comparisons between variables with different scales.

Divide the standard deviation (s) by the mean (x̄). You can express the result as a percentage for easier interpretation.

A higher CV value indicates greater dispersion in the distribution. A lower CV suggests less dispersion and more clustered data.

The CV allows you to directly compare the amount of dispersion in two distributions, even if they have different scales.

If a distribution has a mean of 15 years and a standard deviation of 5 years, the CV would be 33.33%. This means the standard deviation is 33.33% of the mean.

The average value in a dataset where each value is associated with a frequency (how often it occurs).

∑(fXi) / n, where ∑(fXi) is the sum of each score multiplied by its frequency, and n is the number of cases.

A measure of how spread out the data is from the mean, considering frequencies.

√(∑f(Xi - X )^2 / n), where f is the frequency, Xi is the score, X is the mean, and n is the number of cases.

Represents the number of cases with a particular score (frequency of the score).

Represents the individual score.

Represents the mean (average) of the dataset.

Represents the total number of cases in the dataset.