A Review of Descriptive Statistics
By: Johar M. Ashfaque
Tags: Machine Learning, Descriptive Statistics, Deep Learning, Statistics

What is Statistics?

Statistics is the science of collecting data and analysing them to infer proportions that are representative of the population. In other words, statistics is interpreting data in order to make predictions for the population.

There are two branches of Statistics.

DESCRIPTIVE STATISTICS : Descriptive Statistics is a statistics or a measure that describes the data.

INFERENTIAL STATISTICS : Using a random sample of data taken from a population to describe and make inferences about the population is called Inferential Statistics.

We will focus on Descriptive Statistics as it helps to understand the dataset and is an important part of Machine Learning. This is due to Machine Learning being all about making predictions which in turn is only possible following a thorough understanding of the dataset under consideration.

Descriptive Statistics

Descriptive Statistics is summarizing the data at hand through certain numbers like mean, median etc. so as to make the understanding of the data easier and therefore is just the representation of the data available.

The most commonly used measures are

Measures of Central Tendency Measures of Dispersion

Measures of Central Tendency

A Measure of Central Tendency is a one number summary of the data that typically describes the centre of the data. These one number summary are of three types.

Mean which is defined as the ratio of the sum of all the observations in the data to the total number of observations. This is also known as Average. Median which is the point which divides the entire data into two equal halves. One-half of the data is less than the median, and the other half is greater. Median is calculated by first arranging the data in either ascending or descending order.

If the number of observations are odd, median is given by the middle observation in the sorted form.

If the number of observations are even, median is given by the mean of the two middle observation in the sorted form.

3. Mode which is the number which has the maximum frequency in the entire dataset, or in other words, mode is the number that appears the maximum number of times. A data can have one or more than one mode.

If there is only one number that appears maximum number of times, the data has one mode, and is called Uni-modal .

. If there are two numbers that appear maximum number of times, the data has two modes, and is called Bi-modal .

. If there are more than two numbers that appear maximum number of times, the data has more than two modes, and is called Multi-modal.

Unimodal means that the distribution has only one peak, which means it has only one frequently occurring score, clustered at the top. A bimodal distribution has two values that occur frequently (two peaks) and a multimodal has two or several frequently occurring values.

Measures of Dispersion

Measures of Dispersion describes the spread of the data around the Measures of Central Tendency.

Absolute Deviation from Mean also called Mean Absolute Deviation (MAD), describes the variation in the dataset. Variance measures how far are data points spread out from the mean. A high variance indicates that data points are spread widely and a small variance indicates that the data points are closer to the mean of the dataset. Standard Deviation is the square root of the Variance. Range is the difference between the Maximum value and the Minimum value in the dataset. 5. Quartiles are the points in the dataset that divides the dataset into four equal parts. Q1, Q2 and Q3 are the first, second and third quartile of the dataset.

25% of the data points lie below Q1 and 75% lie above it.

50% of the data points lie below Q2 and 50% lie above it. Q2 is nothing but Median.

75% of the data points lie below Q3 and 25% lie above it.

6. Skewness — The measure of asymmetry in a probability distribution is defined by Skewness. It can either be positive or negative.

Positive Skew — This is the case when the tail on the right side of the curve is bigger than that on the left side. For these distributions, mean is greater than the mode.

Negative Skew — This is the case when the tail on the left side of the curve is bigger than that on the right side. For these distributions, mean is smaller than the mode.

If the skewness is zero, the distribution is symmetrical. If it is negative, the distribution is Negatively Skewed and if it is positive, it is Positively Skewed.

7. Kurtosis — Kurtosis describes the whether the data is light tailed (lack of outliers) or heavy tailed (outliers present) when compared to a Normal distribution. There are three kinds of Kurtosis:

Mesokurtic — This is the case when the kurtosis is zero, similar to the normal distributions.

Leptokurtic — This is when the tail of the distribution is heavy (outlier present) and kurtosis is higher than that of the normal distribution.

Platykurtic — This is when the tail of the distribution is light(no outlier) and kurtosis is lesser than that of the normal distribution.

NOTE: The main difference between skewness and kurtosis is that the skewness refers to the degree of symmetry, whereas the kurtosis refers to the degree of presence of outliers in the distribution.