Average Deviation

• An alternative measure of variation that also indicates the average difference between the scores in a distribution and the mean of the distribution

Measure of Variation

• A number that indicates how dispersed scores are around the central point (often the mean) of the distribution

Kurtosis

• How flat or peaked a normal distribution is

• Used to describe the distribution of observed data around the mean

• Measure of whether the data are heavy-tailed or light-tailed relative to a normal distribution; tailedness

Differentiate the Types of Kurtosis

Leptokurtic

• Normal curves that are tall and thin, with only a few scores in the middle of the distribution having a high frequency.

Platykurtic

• Normal curves that are short and more dispersed (broader)

Mesokurtic

• Normal curves that have peaks of medium height and distributions that are moderate in breadth

Skewed Distributions

• Non-normal, non-symmetrical, no bell shape

Normal Distribution

• The mean = median =mode, is the line down the center of the curve

Positive vs Negative Skew

• mean =/ median =/ mode

Negatively Skewed Distribution

• Highest point of curve (the mean) is towards the right

Positively Skewed Distribution

• Highest point of curve (the mean) is towards the left

Normal Curve

• Symmetrical bell-shaped frequency polygon normal distribution

Range

• the difference between the lowest and highest scores in a distribution

Interquartile Range

• The spread of the central 50% of a sample (used with a median)

Standard Deviation

• A measure of how spread out numbers are in a set of values; average difference between the scores and mean of the distribution

Key Concepts

• Differentiate between measures of variation.

• Range: A measure of variation; the difference between the lowest and the highest scores in a distribution

• Interquartile range: the spread of the central  50% of a sample (used with a median) further breaks down bottom half and top half; value between median and lowest and median and highest

• Standard deviation: A measure of how spread out numbers are in a set of values; average difference between the scores and mean of the distribution

• Understand the importance of describing variability

• Explain the difference between a normal distribution and a skewed distribution.

• A normal distribution is a regular curve in the center. A skewed distribution has one tail longer than the other, so it's skewed to the left or right.

• Explain the difference between a positively skewed distribution and a negatively skewed distribution

• In a normal distribution, the mean and the median are the same number while the mean and median in a skewed distribution become different numbers: A left-skewed, negative distribution will have the mean to the left of the median. A right-skewed distribution will have the mean to the right of the median.

• Understand how the mean, median, and mode of a distribution are impacted by positive or negative skew

• Positive Skew: The mode is the high point on the distribution. The median divides the distribution in half. The mean is pulled in the direction of the tail of the distribution; that is, the few extreme scores pull the mean toward them and inflate it.

• Negative Skew: the mean is pulled toward the left by the few extremely low scores in the distribution. As in all distributions, the median divides the distribution in half, and the mode is the most frequently occurring score in the distribution.