3 - representations of data

what is an outlier

an extreme value in a set of data

general formula to find outliers

LOWER OUTLIER:

less than Q₁ - k(IQR)

UPPER OUTLIER:

greater than Q₃ + k(IQR)

k is often 1.5, but in the question they will lyk what to use as k

method of finding outliers using standard deviation

outlier boundaries generally lie ± 2 standard deviations from the mean

the ‘2’ number can also vary from question to question, so they will lyk

what is a box plot

aka box and whisker plot

diagram used to represent key features of a data set

useful for comparing data

how to draw a box plot

box with lines for lower quartile, median and upper quartile

whiskers reaching to smallest and largest value WITHIN OUTLIER BOUNDARIES

crosses (in the picture its dots but draw crosses) outside the diagram = outliers

how to find skew from box plots

ignore whiskers - only look at the central box

what does a cumulative frequency graph look like

points plotted against the upper class boundary of the group (“by the end of this group, we have...”)

0cf point plotted at the lower class boundary of the first group (basically the lowest recorded value)

things you can find with cumulative frequency graphs

median value, UQ value, LQ value, values of any percentiles

for median, go 50% of the way up the y axis then follow it along and the corresponding x value is the answer

same goes for UQ (75%) and LQ (25%) and any percentiles (use the given percentage)

what are histograms used for

to represent grouped continuous data

histogram formula

area is directly proportional to frequency on the graph

how to draw a frequency polygon

join the midpoints of each bar on the histogram with straight lines

what to do if there are gaps in your histogram

use true class boundaries

how to compare data

no. of marks on the question = no. of statements you should make:

• one about an average (mean, median)

• one about spread (range, IQR, SD)

• one about skew

and give a therefore - eg. “therefore the red team are more consistent”

(underlined means should be used with box plot comparisons)

out of mean, median, SD and IQR, what differentiates them

affected by extremes:

• mean

• SD

not affected by extremes:

• median

• IQR