Descriptive Statistics

Descriptive Statistics

are numerical measures that describe a distribution by providing information on the central tendency of the distribution, the width and shape.

Measures of Central Tendency

is a representative number that characterizes the ‘middleness’ of an entire set of data. The 3 measures are mean, median and mode.

Mean

Arithmetic average of a group of scores, calculated by adding all scores divided by the total number of scores.

Median

The middle score in a distribution after scores are arranged from lowest to highest or the other way.

Mode

The score in a distribution that occurs with the greatest frequency.

Measures of Variation

Indicates the degree in which scores are either clustered or spread out in a distribution. Range, Average Deviation, Standard Deviation

Range

The simplest, the difference between the lowest and highest score in a distribution.

Standard Deviation

Average distance of all the scores in the distribution from the mean or central point of the distribution, or the square root of the average squared deviation from the mean.

Average Deviation

The average distance of all the scores from the mean of the distribution.

Kurtosis

How flat or peaked a normal distribution is.

The degree of dispersion among the scores or whether the distribution is tall and skinny or short or flat.

Mesokurtic

have peaks of medium height, distributions are moderate in breadth.

Leptokurtic

tall and thin, with only few scores in the middle of the distribution having a high frequency.

Platykurtic

curves small and more dispersed, many scores around the middle scores that all have similar frequency.

Positively Skewed Distribution

The peak is to the left of the center point, tail extends to the right or in positive direction. Few individuals have extremely high scores that pull the distribution in that direction.

Negatively Skewed Distribution

A distribution in which the peak is to the right of the center point, the tail extends toward the left or in negative direction. Mean is pulled toward the left by the few extremely low scores in the distribution.

z-Scores

is a measure of how many standard deviation units an individual raw score falls from the mean of the distribution. Aa measure of how many standard deviation units an individual raw score falls from the mean of the distribution