## Basic Statistics & Probability – Box & Whisker Plots

Steps 1-3. Draw a box from Q1 to Q3, with a line dividing the box at Q2. Then extend “whiskers” from each end of the box to the extreme values.

### Outliers

Outliers are values that are significantly larger or smaller than the rest of the data; the lowest score (111) appears to be an outlier; outliers must be at least 1.5 times the interquartile range larger than Q3.

## Do you include outliers in a box plot?

Outliers are often visible as dots that are separated from the rest of the plot in box and whisker plots. Here’s a box and whisker plot of the same distribution that does not show outliers.

## What do outliers on a box plot indicate?

Box plots are useful because they show outliers within a data set, which are observations that are numerically different from the rest of the data. An outlier is defined as a data point that is outside the box plot’s whiskers.

## How do you identify outliers?

Visualization is one of the best and easiest ways to have an inference about the overall data and the outliers, and scatter plots and box plots are the most preferred visualization tools to detect outliers.

## What is an outlier in math?

An outlier is a number that is at least two standard deviations from the mean; for example, the outlier in the set would be 1,1,1,1,1,1,1,7,7.

## What is the outlier formula?

The Outlier Formula is a widely used rule that states that a data point is an outlier if it has more than 1.5 IQR below the first quartile or above the third quartile. The first quartile can be calculated as (Q1) = (n 1)/4)th Term.

## How do you explain a Boxplot?

A boxplot is a standardized way of displaying data distributions based on a five-number summary (u201cminimumu201d, first quartile (Q1), median, third quartile (Q3), and u201cmaximumu201d), and it can tell you about your outliers and their values.

## How do box and whisker plots work?

In a box and whisker plot, the lower and upper quartiles are represented by the left and right sides of the box, respectively, and the box covers the interquartile interval, which contains 50% of the data. The median is represented by the vertical line that divides the box in half.

## How do you compare box plots?

Comparison rules for boxplots

- Compare the interquartile ranges (that is, the box lengths) to compare dispersion.
- Look at the overall spread as shown by the adjacent values.
- Look for signs of skewness.
- Look for potential outliers.

## Why are outliers bad?

Outliers are unusual values in your dataset that can cause statistical analyses to be distorted and assumptions to be violated. Outliers increase the variability in your data, which reduces statistical power, so excluding them can cause your results to become statistically significant.

## How do you interpret a box plot skewness?

Skewed data is represented by a lopsided boxplot in which the median divides the box into two unequal pieces; the data is said to be skewed right if the longer part of the box is to the right (or above) the median, and skewed left if the longer part is to the left (or below) the median.

## What is considered an outlier?

In a sense, this definition leaves it up to the analyst (or a consensus process) to decide what will be considered abnormal in a random sample from a population, and these points are often referred to as outliers.