Represent the following data using a box-and-whiskers plot. Exclude the median when computing the quartiles:
NUM
If it helps, you may drag the numbers to put them in a different order. The order isn't checked with your answer. SORTER.init( "sortable" )
Begin by putting the data in order:
\qquad \large{SORTED_DATA.join( ", " )}
Plot the sample minimum (smallest number):
\qquad \large{\color{PINK}{MIN}, SORTED_DATA.slice( 1 ).join( ", " )}
Plot the sample maximum (largest number):
\qquad \large{SORTED_DATA.slice( 0, -1 ).join( ", " ), \color{PINK}{MAX}}
Plot the median (middle number):
\qquad \large{SORTED_DATA.slice( 0, (COUNT - 1) / 2 ).join( ", " ),
\color{PINK}{MEDIAN},
SORTED_DATA.slice( (COUNT + 1) / 2 ).join( ", " )}
Since the data has an odd number of elements, we exclude the median from the list when calculating the quartiles.
Plot the median (middle number):
\qquad \large{SORTED_DATA.slice( 0, COUNT / 2 - 1 ).join( ", " ),
\color{PINK}{SORTED_DATA[COUNT / 2 - 1]},
\color{PINK}{SORTED_DATA[COUNT / 2]},
SORTED_DATA.slice( COUNT / 2 + 1 ).join( ", " )}
The median is the average of the middle numbers, so it's equal to \dfrac{SORTED_DATA[COUNT / 2 - 1] + SORTED_DATA[COUNT / 2]}{2} = MEDIAN
.
Since the data has an even number of elements, we include the middle elements in the list when calculating the quartiles.
Plot the first quartile (halfway between the smallest number and the middle number):
\qquad \large{SORTED_DATA.slice( 0, floor(COUNT / 4) ).join( ", " ),
\color{PINK}{Q1},
SORTED_DATA.slice( floor(COUNT / 4) + 1 ).join( ", " )}
Plot the first quartile (halfway between the smallest number and the middle number):
\qquad \large{SORTED_DATA.slice( 0, floor(COUNT / 4) - 1 ).join( ", " ),
\color{PINK}{SORTED_DATA[floor(COUNT / 4) - 1]},
\color{PINK}{SORTED_DATA[floor(COUNT / 4)]},
SORTED_DATA.slice( floor(COUNT / 4) + 1 ).join( ", " )}
The first quartile is \dfrac{SORTED_DATA[floor(COUNT / 4) - 1] + SORTED_DATA[floor(COUNT / 4)]}{2} = Q1
.
Plot the third quartile (halfway between the middle number and the largest number):
\qquad \large{SORTED_DATA.slice( 0, COUNT - 1 - floor(COUNT / 4)).join( ", " ),
\color{PINK}{SORTED_DATA[COUNT - 1 - floor(COUNT / 4)]},
SORTED_DATA.slice( COUNT - floor(COUNT / 4) ).join( ", " )}
Plot the third quartile (halfway between the middle number and the largest number):
\qquad \large{SORTED_DATA.slice( 0, COUNT - floor(COUNT / 4) - 1).join( ", " ),
\color{PINK}{SORTED_DATA[COUNT - floor(COUNT / 4) - 1]},
\color{PINK}{SORTED_DATA[COUNT - floor(COUNT / 4)]},
SORTED_DATA.slice( COUNT - floor(COUNT / 4) + 1 ).join( ", " )}
The third quartile is \dfrac{SORTED_DATA[COUNT - floor(COUNT / 4) - 1] + SORTED_DATA[COUNT - floor(COUNT / 4)]}{2} = Q3
.
Your box-and-whisker plot should look like the example below the number line.