# Statistical and graphical analysis: univariate analysis

When we talk about univariate analysis, we will normally find elements such as:

• Histograms.
• Percentiles: The percentile (or centile) is the value of the variable below which a certain percentage of observations fall; for example, the 20th percentile is the value (or score) below which 20 per cent of the observations fall.
• Statistical moments: Mean, median, standard deviation.
• The moment above zero: Mean, median, second moment.
• Moments above the mean: Variance, standard deviation, skewness, kurtosis.

In the statistical and graphical analysis, specifically in the univariate analysis, we can observe two main elements to take into account:

• Kurtosis: The fourth central moment is whether the distribution is tall and thin or short and square, compared to the normal distribution of the same variance.
• Skewness: The measure of the skewness of the probability distribution of a real-valued random variable. The value of skewness can be positive or negative or even undefined. Qualitatively, a negative skewness value indicates that the tail of the left-hand side of the probability density function is longer than that of the right-hand side. Most of the values (possibly including the median) lie to the right of the mean.

## Kurtosis

From the highest peak to the lowest peak:

Kurtosis: Leptokurtic, Mesokurtic and Platykurtic:

• Leptokurtic: “Lepto” (meaning thin). In terms of shape, a leptokurtic distribution has a sharper peak around the mean.
• Mesocurtic: Semicircular distribution. Elevation in the cosine distribution. Uniform distribution.
• Platicurtic: “Plati” comes from tabla. It has a platicurtic distribution with a lower and broader peak around the mean in terms of shape.