Descriptive Statistics and Variability Measures

This flashcard set covers key concepts in descriptive statistics, measurements of central tendency, measures of variability, distributions, and graphical representations, providing comprehensive preparation for exams in these topics.

Descriptive Statistics

Used to characterize the shape, central tendency, and variability of a data set.

Frequency Distribution

The total set of scores for a particular variable.

N

Total number of scores in a sample.

n

Number of subjects in subsets of a sample.

Frequency Distribution

Displays the number of times each score occurred.

Percentages

Can display frequency as percentages of the total distribution.

Grouped Frequency Distribution

Used with continuous data, represents ranges of scores.

Histogram

A bar graph used to represent frequency distributions.

Line Plot

A graphical representation of grouped data frequencies.

Stem-and-Leaf Plot

A method of displaying quantitative data in a graphical format.

Normal Distribution

A distribution where most scores fall in the middle.

Skewed Distribution

A distribution where one tail is longer or fatter than the other.

Positive Skew

A distribution with a tail pointing to the right.

Negative Skew

A distribution with a tail pointing to the left.

Measure of Central Tendency

Describes the 'typical' nature or center of the data.

Mode

The score that occurs most frequently in a distribution.

Median

The middle score in a distribution when arranged in order.

Mean

The sum of scores divided by the number of scores.

Central Tendency and Skewness

Mean is affected by extreme scores; median is usually between mean and mode.

Range

Difference between the highest and lowest values in a data set.

Percentiles

Divide data into 100 equal portions.

Quartiles

Divide data into 4 equal parts.

Interquartile Range

Distance between the 25th and 75th percentiles.

Deviation Score

Distance each score is from the mean.

Sum of Squares (SS)

Sum of the squared deviation scores.

Variance

Mean of the squared deviation scores.

Standard Deviation

Square root of variance, measures variability in original units.

Coefficient of Variation (CV)

Ratio of the standard deviation to the mean, expressed as percentage.

Normal Curve

Represents a theoretical concept with mean, median, and mode equal.

Z-Score

Expresses how many standard deviations a score is from the mean.

T-Score

Compares bone mineral density to a healthy adult population.

BMD

Bone Mineral Density is measured in g/cm².

Osteopenia

Condition with a T-Score between -2.5 and -1.0.

Osteoporosis

Condition with a T-Score less than -2.5.

Grouped Frequency Distribution Example

Ranges such as 95-100, 90-94 for continuous data.

Graph of a Histogram

A pictorial representation using bars to show frequencies.

Line Plot Graph Example

Displays frequencies of grouped data in line form.

Stem-and-Leaf Example

Shows data distribution with stem values and leaf details.

Shaped Distribution Types

Includes normal, positively skewed, and negatively skewed.

Mean Calculation

Sum of scores divided by the total number of scores.

Median Calculation

Middle score when data is ordered, using the average of middle scores if even.

Mode Calculation

Identified visually or numerically from frequency distribution.

Standard Deviation Formula

s = √(SS/(n - 1)) to compute standard deviation.

Population Variance Symbol

Written as σ² (sigma squared).

Sample Variance Calculation

s² = SS/(n - 1), adjusts for sample size.

Box Plot

Graphical illustration representing percentiles and quartiles.

Range Limitation

Does not show variability within extreme scores.

Deviation Score Calculation

X - X̄ to find the distance from the mean.

Sum of Squared Deviation Scores Purpose

Helps increase understanding of data variability.

Normal Distribution Characteristic

Mean, median, and mode are equal and located at the center.

Area under the Normal Curve

Percentage of data within specified standard deviation ranges.

Z-Score Calculation

z = (X - X̄) / s to determine standard deviation units.

Z-Scores and Bone Density Relationship

Compares individual bone density against population norms.

T-Score Risk Categories

Defines bone health as high BMD, normal, osteopenia, or osteoporosis.

Intra-Quartile Range Representation

Shows middle 50% of data in box plots.

Coefficient of Variation Importance

Useful for comparing variability across different data distributions.

Mean Influence on Skewness

Mean is pulled towards the tail in skewed distributions.

Percentile Rank Interpretation

Indicates relative standing within a data set.

Use of Frequency Distribution in Statistics

Assists in understanding data landscape and patterns.

Grouped Data Frequency Visualization

Creates understanding of score distributions in segments.

Histogram Characteristics

Visual representation focusing on the range and frequency of scores.

Standard Deviation in Reporting

Typically used in expressing results to indicate variability.

Understanding Bone Density Values

Important for classifying risk and health conditions.

Measures for Comparing Data Variability

Involves standard deviation, variance, and coefficient of variation.

Significance of Skewed Data Interpretation

Alerts to the need for careful analysis of data trends.

Bimodal Distribution Definition

A frequency distribution with two modes occurring.

Multimodal Distribution Definition

A frequency distribution with two or more modes.

Graphical Tools for Data Analysis

Includes histograms, box plots, and line plots for visualization.

Statistical Interpretation of Z Scores

Helps identify how unusual a score is relative to the mean.

Understanding Variability in Descriptive Statistics

Characterizes how spread out or clustered data scores are.

Identifying Statistical Measures

Mean, median, mode, range, variance, and standard deviation are key.

Application of Statistics in Research

Facilitates conclusions about populations based on sample data.

Limitations of Mean in Skewed Data

Mean alone may misrepresent the center of distribution.

Importance of Graphical Representation in Data Understanding

Aids in quickly grasping complex data sets through visual formats.

Understanding Shapes of Data Distributions

Helps identify normality, skewness, and frequency patterns.

Percentile Calculation Example

P92 indicates a score above 92% of the population.

Visualizing Data Ranges in Box Plots

Clearly distinguishes between different quartiles and median.

Variability's Role in Statistical Analysis

Essential for understanding populations and making predictions.

Mean and Standard Deviation Interpretation in Reports

Describes central tendency and spread of the data respectively.

Frequency Distribution to Summarize Data

Provides a summarized view of how data points are spread out.

Quantifying Elements of Data Distributions

Involves measuring central tendency, shape, and variability.

Understanding the Context of Data Findings

Enables better interpretation of statistical results.

Standard Deviation and Mean Relationship

Can reflect the overall distribution stability or variability.