## 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.

## How do you use an outlier in a box and whisker plot?

The data value must be the following to be considered an outlier:

- Larger by at least 1.5 times the interquartile range (IQR) than Q3, or smaller by at least 1.5 times the IQR than Q1.

## How are box plots affected by outliers?

Outliers are significant because they are numbers that are “outside” of the Box Plot’s upper and lower fences; even though they do not affect or change any other numbers in the Box Plot, your instructor will want you to find them. To find your fences, multiply your IQR by 1.5.

## How do you plot outliers?

The median of the upper half of the data set is the upper quartile (Q3), and the interquartile range (IQR) is the spread of the middle 50% of the data values. Lower Limit = Q1 u2013 1.5 IQR. Outliers are any values that are greater than the upper limit or less than the lower limit.

## What do outliers on a box plot indicate?

Outliers are values that are more than one-and-a-half times the length of the box from either end of the box in a box-and-whisker plot.

## 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.

## 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.

## How do you determine if there are outliers?

When we subtract 1.5 x IQR from the first quartile, any data values less than this number are considered outliers, and when we add 1.5 x IQR to the third quartile, any data values greater than this number are also considered outliers.

## 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.

## What is the 1.5 IQR rule?

Subtract 1.5 x (IQR) from the first quartile; any number less than this is a suspected outlier. Add 1.5 x (IQR) to the third quartile; any number greater than this is a suspected outlier.

## How do you calculate a box plot?

Calculate the interquartile range (the difference between the upper and lower quartile) and call it IQ. The line from the lower quartile to the smallest point that is greater than L1 is now drawn from the lower quartile to the smallest point that is greater than L1.

## What does the length of a box plot mean?

The length of the box indicates sample variability, and the line across the box indicates where the sample is centred; the position of the box in its whiskers, as well as the position of the line in the box, also indicates whether the sample is symmetric or skewed to the right or left.

## How do box plots work?

A box and whisker plot, also known as a box plot, shows a five-number summary of a set of data by drawing a box from the first to third quartile, a vertical line through the box at the median, and whiskers from each quartile to the minimum or maximum.

## What are outliers in Math?

An outlier is a value in a data set that differs significantly from the other values, or values that are unusually far from the middle. There is no rule for identifying outliers, but some books define an outlier as a value that is more than 1.5 times the value of the interquartile range beyond the quartiles.