The five number summary, box plots, & outliers

The five number summary, boxplots, & outliers

The five number summary

• Gives is a way to describe a distribution using only five numbers

• Minimum

• 1st quartile

• median

• 3rd quartile

• Maximum

Minimum

• the smallest value in a data set

1st quartile

• is the median of the bottom half

• it is a position where 25% of the data values are below it & 75% of the data values are larger than it

• the first quartile is essentially the median of the median

median

• is the middle data value

• is a point at which 50% of the data values are below the median, & 50% of the data value is larger the median.

3rd quartile

• is the median of the top half which gives us the third quartile

• it is a position where 75% of the data values are below it, & 25% percent of the data values are larger than the third quartile

Maximum

• is the largest value in a data set

Five number summary gives us

• a way to divide the data into four equal quarters

The formula of first quartile = Q1

position of Q1 = n+1/ 2

IMPORTANT n refers to the values BELOW the median

in this case Q1 is 25

The formula of the third quartile = 3Q

Position of Q3 = n+1/2

IMPORTANT n refers to the number of data values that are ABOVE the median

in this case Q3 is 36

BOXPLOT

• gives us a visual representation of the five number summary

  

• each vertical line on the box plot represents a number from the five number summary

• the horizontal line that extends ends out from the box are called whiskers

• the box itself is called interquartile range & refers to the middle 50% of an order data set & its equal to the third quartile (Q3) subtracted by first quartile (Q1)

Interquartile range

the box itself in a boxplot

Modified boxplot

• uses five number summary, but accounts for outliers → if there are outliers a whisker or both whiskers will extend to the new minimum or maximum