Statistics 3.4 - (The Five-Number Summary: Boxplots)

Quartiles (4 parts)

Percentiles other than the median that are the 25th, 50th, and the 75th percentiles

pth percentile (p stands for percentage)

is the number that divides the bottom p% of the data from the top (100 -p)%

Quintiles (5 parts)

Percentiles other than the median that are the 20th, 40th, 60th, and 80th percentiles

First quartile Q₁

The median of the bottom half of the data

Second quartile Q₂

The median of the entire data set

Third quartile Q₃

The medin of the top half of the data set

Uniform quartlies

All quartiles are 25% and straight

Bell-shaped quartiles

All quartiles are 25% and is bell-shaped

Right-skewed quartiles

All quartiles are 25% and aiming towards the left

Left-skewed quartiles

All quartiles are 25% and aiming towards the right

First step of solving quartiles

Arrange data in increasing order

Second step of solving quartiles

Find the median of the entire data set (this will be Q₂)

Third step of solving quartiles

Divide the ordered data into two halves, a bottom half and a top half (If the number of observations is odd, include the median in both halves)

Fourth step of solving quartiles

Find the median of the bottom half of the data set (this is Q₁)

Fifth step of solving quartiles

Find the median of the top half of the data set (this is Q₃)

Sixth step of solving quartiles

Summarize the results (write down Q₁, Q₂, Q₃ )

Interquartile range (IQR)

The difference between the first and third quartiles; that is, IQR = Q₃ — Q₁

Five-number summary

Min, Q₁, Q₂, Q₃, Max

Lower limit

Q₁ — 1.5 x IQR

Upper limit

Q₃ + 1.5 x IQR