Descriptive Statistics

Flashcards for lecture notes on descriptive statistics, covering distributions, graphical representations, data summarization, central tendency, dispersion, and distribution shape.

Frequency Distribution

Shows the values a variable can take and the number of records with each value.

Relative Frequency Distribution

Obtained by dividing each frequency by the total number of responses, showing the proportion of responses of each type.

Cumulative Frequency Distribution

Obtained by adding the frequency in a given category to those of the categories showing a lesser level of the measured variable.

Cumulative Relative Frequency Distribution

Calculated by dividing each cumulative frequency by the total number of observations or responses.

Bar Chart

Illustrates frequencies and relative frequencies of qualitative data, with bar lengths proportional to frequencies.

Pie Chart

Illustrates frequencies and relative frequencies of qualitative data, dividing a circle so that the areas of the sectors are proportional to the frequencies.

Histogram

Consists of contiguous bars used to depict relative frequencies of continuous, usually grouped, data.

Polygon

Constructed similarly to histograms, placing a dot at a height appropriate to the y axis for each interval.

Stem-and-Leaf Plot (Stemplot)

Preserves the values of the displayed variable, dividing each observation into a stem and leaf component.

Box and Whisker Plot (Boxplot)

Presents the shape of a skewed distribution, dividing data points into quartiles.

Proportion

A fraction in which the numerator is a subset of the denominator, often expressed in percentage.

Rate

A complex fraction with a numerator, a denominator, and a stated time period.

Ratio

A value obtained by dividing one number by another; the numbers can be either related or unrelated.

Mean

The average number, calculated as the sum of all values divided by the number of values.

Mode

The score or scores in a set that occur most frequently.

Median

The middle value in a data set when the observations are arranged in increasing or decreasing order.

Geometric Mean

The mean or average of a set of data measured on a logarithmic scale.

Harmonic Mean

The number of observations divided by the sum of reciprocals of the values of the set of observations.

Range

The difference between the largest and smallest observations in a sample.

Variance

The average of the squared deviations of the data from the mean.

Standard Deviation

The positive square root of the variance.

Interquartile Range

The difference between the upper and lower quartiles.

Coefficient of Variation

Expresses standard deviation as a percentage of the sample mean.

Skewness

The degree of asymmetry of a distribution; can be negatively or positively skewed.

Kurtosis

The peakedness of a distribution; can be leptokurtic (sharp peak) or platykurtic (flattened middle).