(copy) The Exciting Tale of Statistics

Positive skew: The right tail is longer and the mass of the distribution is concentrated on the left of the figure. The distribution is said to be right-skewed. Negative skew: The left tail is longer and the mass of the distribution is concentrated on the right of the figure. The distribution is said to be left-skewed.

A&nbsp;skewed distribution&nbsp;is a distribution in which there is no such mirror-imaging. For&nbsp;skewed distributions, it is quite common to have one tail longer or drawn out relative to the other tail. A "skewed right"distribution&nbsp;is one in which the tail is on the&nbsp;right side.

WHAT IS A RIGHT SKEWED DISTRIBUTION?

WHAT NEEDS TO BE DONE TO DETERMINE THE SHAPE OF THE DISTRIBUTION?

HOW DO YOU DESCRIBE THE SHAPE OF A DISTRIBUTION?

WHAT ARE CATEGORICAL VARIABLES?

WHAT IS THE FIVE-NUMBER SUMMARY USED FOR?

WHAT IS STANDARD DEVIATION A MEASURE OF?

An&nbsp;outlier&nbsp;is an observation that lies an abnormal distance from other values in a random sample from a population. In a sense, this definition leaves it up to the analyst (or a consensus process) to decide what will be considered abnormal. Before abnormal observations can be singled out, it is necessary to characterize normal observations.

The&nbsp;shape of a distribution&nbsp;is&nbsp;described&nbsp;by its number of peaks and by its possession of symmetry, its tendency to skew, or its uniformity. (Distributions&nbsp;that are skewed have more points plotted on one side of the graph than on the other.)

The center is the median and/or mean of the&nbsp;data. The spread is the range of the data. And, the&nbsp;shape&nbsp;describes the type of graph. The four ways to&nbsp;describe shape are whether it is symmetric, how many peaks it has, if it is skewed to the left or right, and whether it is uniform.

How can I describe the shape of a distribution?

The&nbsp;shape&nbsp;of a&nbsp;distribution&nbsp;is described by its number of peaks and by its possession of symmetry, its tendency to skew, or its uniformity. (Distributions that are skewed have more points plotted on one side of the graph than on the other.)

The Shape of the Distribution tells us which of the descriptive statistics we should be using. Though we have three measures of central tendency, they are not all appropriate for all situations.

Common Distribution Shapes 1. Symmetric Distribution 2. Skewed Distribution 3. Bimodal Distribution 4.&#160; Kurtosis

Five-number summary is type of summary about the statistical data. It is defined in descriptive statistics. It is a theory which provides information about the given set of values. It is especially useful in descriptive analyses or during the preliminary investigation of a large data set.

The five-number summary is a concise information about the distribution of the values among a set of observations. It provides various information such as spread of the data, location of the median, smallest and biggest values, range of the data etc.&nbsp;

It is also useful in ratio and interval measurements. By the use of this summary, it becomes possible to easily compare different sets of data by making comparisons with different five-number summaries which can also be illustrated graphically.

A summary consists of five values: the most extreme values in the data set (the maximum and minimum values), the lower and upper quartiles, and the median. These values are presented together and ordered from lowest to highest: 1)&nbsp;Minimum:&nbsp;The minimum indicates the smallest value in the data set. It is represented by "min". 2)&nbsp;Maximum:&nbsp;The maximum denotes the biggest value lying in the given data set. It is notified by "max". 3) Lower Quartile:&nbsp;&nbsp;It is a point that separates first 25% (or lowest 25%) of the values from the rest 75% of the values of the given data. First quartile is also known as lower quartile and is denoted by Q1. 4) Median:&nbsp;Median is the value that falls exactly in the middle of the data set. In other words, median is a middle most value when the observations are arranged in ascending order. It is sometimes denoted by Q2&nbsp;(second quartile). 5) Upper Quartile:&nbsp;&nbsp;Upper quartile is the value that separates out biggest 25% values from the rest 75%. It is represented by Q3&nbsp;and is also called as third quartile.

the standard deviation measures how spread out numbers are from an average value. Standard deviation&nbsp;can be calculated by taking the square root of the variance, which itself is the average of the squared differences of the mean.

Variables&nbsp;can be classified as categorical&nbsp;(aka, qualitative) or quantitative aka, numerical). Categorical. Categorical variables take on values that are names or labels. The color of a ball (e.g., red, green, blue) or the breed of a dog (e.g., collie, shepherd, terrier) would be examples of categorical variables.

THE EXCITING TALE OF&nbsp;STATISTICS&nbsp;

Chapter 1...........How do you describe the shape of a distribution Chapter 2...........What are outliers Chapter 3...........What is standard deviation a measure of Chapter 4...........What needs to be done to determine the shape of the distribution Chapter 5...........What is the five-number summary used for Chapter 6...........What are categorical variables Chapter 7...........What is a right skewed distribution