Descriptive Statistics Overview

The sum of all scores divided by the total number of scores.

The average of a set of data.

The middle value in an ordered dataset; divides scores into two halves (50% below, 50% above).

Arrange scores in order and find the middle score (or average of two middle scores if n is even).

Another name for the median.

The mean is stable because each score affects it; the sum of distances from the mean is zero.

Use Mean when sampling stability is important and other measures (like standard deviation) are needed.

Values that characterize the center or average of a dataset.

1. Arrange the data in ascending order.
2. If the number of values is odd, the median is the middle value.
3. If the number of values is even, the median is the average of the two middle values.

The score that appears most frequently in a dataset.

Distributions can be unimodal (one mode), bimodal (two modes), trimodal (three modes), or multimodal (more than three modes).

The median is:

• Not affected by extreme values.
• Can be used for ordinal level data.

Use the median when:

• You want the exact midpoint of the data distribution.
• There are extreme scores in the dataset.

The mode is:

• Applicable for both qualitative and quantitative data.
• May not be unique (multiple modes).
• Can be affected by extreme values.
• May not exist.

Use the mode when:

• You want the most frequent or 'typical' value in the data.
• Data is measured on a nominal scale.

Divide a ranked dataset into four equal parts, with Q1 representing the 25th percentile, Q2 the 50th percentile (median), and Q3 the 75th percentile.

Divide a ranked dataset into ten equal parts, with D1 representing the 10th percentile, D2 the 20th percentile, and so on.

Divide a ranked dataset into one hundred equal parts, with P1 representing the 1st percentile, P2 the 2nd percentile, and so on.

A general term for measures that divide a ranked dataset into equal parts, like quartiles, deciles, and percentiles.

Describe the spread or dispersion of data points in a dataset, indicating how clustered or scattered scores are.

Central tendency (like mean, median, mode) describes the center of the data, while variability measures how spread out the data is around that center.

Measures the degree to which scores are clustered or spread out in a distribution.

Indicates how well an individual score or sample represents the entire population based on the spread of data.

A table that shows the relationship between two or more variables. It displays the frequency of each combination of categories for the variables being examined.

A graph that uses rectangular bars to represent data points. The height of each bar corresponds to the value it represents.

A graph that uses connected lines to represent data points over time or another continuous variable.

A circular graph that uses slices of a circle to represent proportions of a whole.

A method of displaying data that shows the proportion of each category relative to the total.

The difference between the highest and lowest values in a dataset.

The range of values between the first quartile (Q1) and the third quartile (Q3), representing the middle 50% of the data.

The average distance of each value from the mean, ignoring direction (positive or negative).

The average of the squared differences between each value and the population mean.

The square root of the population variance.

The average of the squared differences between each value and the sample mean, adjusted by dividing by (n-1) to account for sample size.

The square root of the sample variance.

A measure of how many standard deviations a data point is away from the mean. It tells us how much a specific data point deviates from the average, in standard deviation units.

The location of a score with respect to other scores in a dataset, often indicated by z-scores.

Measures the relative dispersion of data, expressed as a percentage. It compares the standard deviation to the mean, showing how much the data varies relative to its average value.

Indicates the asymmetry of a distribution. A distribution is skewed if it leans heavily towards one side, making it non-symmetrical.

The tail of the distribution is longer on the right side, indicating more extreme values above the mean.

The tail of the distribution is longer on the left side, indicating more extreme values below the mean.

Measures the peakedness or flatness of a distribution, reflecting how concentrated the data is around the mean.

Various methods used to present data visually and numerically, including narratives, tables, and graphs.