How to Read a Horizontal Box Plot
What does a box plot tell y'all?
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 nautical chart often used in explanatory information assay. Box plots visually show the distribution of numerical data and skewness through displaying the data quartiles (or percentiles) and averages.
Box plots show the five-number summary of a set up of data: including the minimum score, first (lower) quartile, median, third (upper) quartile, and maximum score.
Definitions
Minimum Score
The lowest score, excluding outliers (shown at the end of the left whisker).
Lower Quartile
Xx-v pct of scores fall below the lower quartile value (besides known as the get-go quartile).
Median
The median marks the mid-signal of the data and is shown by the line that divides the box into 2 parts (sometimes known as the second quartile). Half the scores are greater than or equal to this value and one-half are less.
Upper Quartile
Seventy-five percent of the scores fall below the upper quartile value (also known as the 3rd quartile). Thus, 25% of information are above this value.
Maximum Score
The highest score, excluding outliers (shown at the stop of the right whisker).
Whiskers
The upper and lower whiskers correspond scores outside the middle 50% (i.due east. the lower 25% of scores and the upper 25% of scores).
The Interquartile Range (or IQR)
This is the box plot showing the center fifty% of scores (i.e., the range betwixt the 25th and 75th percentile).
Why are box plots useful?
Box plots divide the data into sections that each contain approximately 25% of the data in that set.
Box plots are useful as they provide a visual summary of the data enabling researchers to quickly identify mean values, the dispersion of the information set, and signs of skewness.
Annotation the image in a higher place represents information which is a perfect normal distribution and most box plots will not arrange to this symmetry (where each quartile is the same length).
Box plots are useful as they show the average score of a data set.
The median is the boilerplate value from a set of data and is shown by the line that divides the box into ii parts. Half the scores are greater than or equal to this value and one-half are less.
Box plots are useful as they show the skewness of a information set
The box plot shape volition show if a statistical information set is normally distributed or skewed.
When the median is in the middle of the box, and the whiskers are well-nigh the aforementioned on both sides of the box, then the distribution is symmetric.
When the median is closer to the lesser of the box, and if the whisker is shorter on the lower end of the box, and then the distribution is positively skewed (skewed right).
When the median is closer to the top of the box, and if the whisker is shorter on the upper end of the box, then the distribution is negatively skewed (skewed left).
Box plots are useful every bit they prove the dispersion of a data fix.
In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed.
The smallest value and largest value are establish at the end of the 'whiskers' and are useful for providing a visual indicator regarding the spread of scores (e.g. the range).
The interquartile range (IQR) is the box plot showing the middle l% of scores and tin can be calculated by subtracting the lower quartile from the upper quartile (e.g. Q3−Q1).
Box plots are useful equally they show outliers within a data fix.
An outlier is an observation that is numerically afar from the rest of the data.
When reviewing a box plot, an outlier is divers as a information point that is located outside the whiskers of the box plot.
Source: https://towardsdatascience.com/agreement-boxplots-5e2df7bcbd51
For case, exterior 1.5 times the interquartile range above the upper quartile and below the lower quartile (Q1 - i.5 * IQR or Q3 + one.v * IQR).
How to compare box plots
Box plots are a useful way to visualize differences amongst different samples or groups. They manage to provide a lot of statistical data, including — medians, ranges, and outliers.
Note, although box plots take been presented horizontally in this article, it is more common to view them vertically in enquiry papers
Step 1: Compare the medians of box plots
Compare the respective medians of each box plot. If the median line of a box plot lies exterior of the box of a comparison box plot, then there is probable to exist a difference between the ii groups.
Source: https://blog.bioturing.com/2018/05/22/how-to-compare-box-plots/
Footstep ii: Compare the interquartile ranges and whiskers of box plots
Compare the interquartile ranges (that is, the box lengths), to examine how the information is dispersed betwixt each sample. The longer the box the more dispersed the data. The smaller the less dispersed the data.
Next, look at the overall spread as shown past the extreme values at the end of two whiskers. This shows the range of scores (another type of dispersion). Larger ranges point wider distribution, that is, more scattered information.
Step three: Look for potential outliers (see above paradigm)
When reviewing a box plot, an outlier is defined as a information betoken that is located outside the whiskers of the box plot.
Footstep 4: Look for signs of skewness
If the data do not announced to exist symmetric, does each sample show the aforementioned kind of asymmetry?
How to reference this article:
How to reference this commodity:
McLeod, Due south. A. (2019, July xix). What does a box plot tell y'all? Simply psychology: https://www.simplypsychology.org/boxplots.html
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How to Read a Horizontal Box Plot
Source: https://www.simplypsychology.org/boxplots.html
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