# What does a box plot show about variability?

## What does a box plot show about variability?

A boxplot invites you to characterize variation in many different ways, by comparing the quantities shown on the plot: extremes, extremes of the whiskers, quartiles, and median. That gives 21 different measures of variation in each one!

How do you compare variability in a boxplot?

Guidelines for comparing boxplots

1. Compare the respective medians, to compare location.
2. Compare the interquartile ranges (that is, the box lengths), to compare dispersion.
3. Look at the overall spread as shown by the adjacent values.
4. Look for signs of skewness.
5. Look for potential outliers.

Which box plot shows more variability?

Taller boxes imply more variable data. That’s something to look for when comparing box plots, especially when the medians are similar. Wider ranges (whisker length, box size) indicate more variable data.

### Do box plots show variance?

You see, box plot is a very powerful tool that we have for understanding our data. Using box plots we can better understand our data by understanding its distribution, outliers, mean, median and variance. Box plot packs all of this information about our data in a single concise diagram.

What does variability mean in statistics?

Descriptive statistics: measures of variability Variability refers to how spread scores are in a distribution out; that is, it refers to the amount of spread of the scores around the mean. For example, distributions with the same mean can have different amounts of variability or dispersion.

How do you explain boxplot results?

The median (middle quartile) marks the mid-point of the data and is shown by the line that divides the box into two parts. Half the scores are greater than or equal to this value and half are less. The middle “box” represents the middle 50% of scores for the group.

## How do you explain Boxplot results?

How do you find the results of a box plot?

What do box plots show?

A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum. A vertical line goes through the box at the median. The whiskers go from each quartile to the minimum or maximum.

### Why is variability important in statistics?

Variability serves both as a descriptive measure and as an important component of most inferential statistics. In the context of inferential statistics, variability provides a measure of how accurately any individual score or sample represents the entire population.

How do you show variability in data?

Measures of Variability: Variance

1. Find the mean of the data set.
2. Subtract the mean from each value in the data set.
3. Now square each of the values so that you now have all positive values.
4. Finally, divide the sum of the squares by the total number of values in the set to find the variance.

What are the values in a box plot?

They also show how far the extreme values are from most of the data. A box plot is constructed from five values: the minimum value, the first quartile, the median, the third quartile, and the maximum value. We use these values to compare how close other data values are to them.

## How is a box plot used in Explanatory Analysis?

By Saul McLeod, published 2019 What is a box plot? In descriptive statistics, a box plot or boxplot (also known as box and whisker plot) is a type of chart often used in explanatory data analysis. Box plots visually show the distribution of numerical data and skewness through displaying the data quartiles (or percentiles) and averages.

What can a boxplot shape tell you about a statistical data set?

What the boxplot shape reveals about a statistical data set. A boxplot can show whether a data set is symmetric (roughly the same on each side when cut down the middle) or skewed (lopsided). A symmetric data set shows the median roughly in the middle of the box.

How is the median shown in a boxplot?

The median, part of the five-number summary, is shown by the line that cuts through the box in the boxplot. Skewed data show a lopsided boxplot, where the median cuts the box into two unequal pieces.