Quartiles and Box plots (Distribution graph)

It’s also called Box and whisker plots, or Five-number summary.

▶︎ Jump over to Khan academy for practice: Comparing data distributions

Refer to Khan academy: Reading box plots
Refer to Khan academy: Interpreting box plots
Refer to Maths is for fun: Quartiles

Quartiles are the values that divide a list of numbers into quarters:

• Put the list of numbers in order
• Then cut the list into 4 equal parts
• The Quartiles are at the “cuts”

or

Interquartile range (IQR) (Box plot)

Refer to Khan academy.

The Interquartile Range is from Q1 to Q3:

Example

Five-number summary

Refer to Khan academy: Five-number summary

Example

Box and Whisker Plot

Box and Whisker Plot can show all the important values.

Important values:

• Median: at Q2
• Interquartile Range: Q3-Q1
• Highest
• Lowest
• Shape: Skewed Left or Right if Q2 IS NOT in the middle of the Interquartile range.
• Mean: It DOES NOT show mean in the Box Plot unless it’s a Normal Distribution which mean=median.

Find out the Mean in Box plot

Although we can’t find out the mean value from the Box Plot. But according to the position of the Q2 (the Median), we could know the relationship between the Mean & Median:

• If Q2 is at the middle in the Interquartile, it's probable a Normal Distribution, which Median = Mean
• If Q2 is at the LEFT in the Interquartile, it's probable a Right Skewed Distribution, which Median < Mean
• If Q2 is at the RIGHT in the Interquartile, it's probable a Left Skewed Distribution, which Median > Mean

Example

Example

At this graph below, according to the Q2 position, we know that the distribution shape is Skewed right

Practice

Practice

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