2. Measures of Dispersion
• Measures of dispersion quantify the spread, variability, or dispersion of a
dataset. They provide insights into how the individual values in a dataset
deviate from the central tendency (mean, median, etc.).
3. Range
• The Range is the distance covered by the scores in a distribution, from the
smallest score to the largest score.
• Range= Xmax – Xmin
• If the scores have values from 1 to 5, for example, the range is 5.5 – 0.5 5
points.
4. Standard Deviation And Variance
• The standard deviation is the most commonly used and the most important
measure of variability. Standard deviation uses the mean of the distribution as
a reference point and measures variability by considering the distance
between each score and the mean.
• Deviation is distance from the mean
5. Mean Deviation
• Mean deviation, also known as the average deviation, is a measure of the
dispersion or spread of a set of values. It quantifies how much individual
values in a dataset deviate from the mean (average) of the dataset.
6. Quartile Deviation
• Quartile deviation, also known as semi-interquartile range, is a measure of
statistical dispersion that describes the spread of a dataset. The quartile
deviation is calculated as half the difference between the upper quartile (Q3)
and the lower quartile (Q1).
7. Variance
• Variance is a statistical measure that quantifies the spread or dispersion of a
set of values in a dataset. It provides insight into how individual data points
differ from the mean (average) of the dataset.
8. Standard Deviation
• Standard deviation is the square root of the variance and provides a
measure of the standard, or average, distance from the mean.
9. Normal & Binomial Distribution
• Normal distribution and binomial distribution are two fundamental
probability distributions used in statistics to model different types of
phenomena.
10. Normal Distribution
• Shape: The normal distribution, also known as the Gaussian distribution,
forms a symmetric bell-shaped curve.
11. Binomial Distribution
• Shape: The binomial distribution is discrete and represents the number of
successes in a fixed number of independent Bernoulli trials.
• Each trial has only two possible outcomes: success (usually denoted as 1) or
failure (usually denoted as 0).
12. z Score
• Statisticians often identify sections of a normal distribution by using
z-scores. A normal distribution with several sections marked in z-score units.
The z-scores measure positions in a distribution in terms of standard
deviations from the mean. (Thus, z = 1 is 1 standard deviation above the
mean, z = 2 is 2 standard deviations above the mean, and so on.)
13. Skewness
• Definition: Skewness is a measure of the asymmetry of a probability
distribution. It indicates whether the data is skewed to the left (negatively
skewed), to the right (positively skewed), or symmetric.
14. Kurtosis
• Definition: Kurtosis measures the "tailedness" of a probability distribution.
It indicates whether the data has heavy tails or light tails compared to a
normal distribution.
