Everything Maths Grade 11

18.3 CHAPTER 18. STATISTICS

4. Consider a set of data that gives the results of 20 pupils in a class.

(a) When is the data seen as a population?

(b) When is the data seen as a sample?

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(1.) 015e (2.) 015f (3.) 015g (4.) 015h

18.3 Graphical Representation of Measures of Central Tendency and Dispersion

EMBDX

The measures of centraltendency (mean, median, mode) and the measures of dispersion (range,semi-

inter-quartile range, quartiles, percentiles, inter-quartile range) are numerical methods of summarising

data. This section presents methods of representing the summarised data using graphs.

Five Number Summary EMBDY

One method of summarising a data set is to present a five number summary. The five numbers are:

minimum, first quartile,median, third quartile and maximum.

Box and Whisker Diagrams EMBDZ

A box and whisker diagram is a method ofdepicting the five number summary, graphically.

The main features of thebox and whisker diagramare shown in Figure 18.2. The box can lie horizon-

tally (as shown) or vertically. For a horizontal diagram, the left edge ofthe box is placed at thefirst

quartile and the right edge of the box is placed at the third quartile. Theheight of the box is arbitrary,

as there is no y-axis. Inside the box there is some representation of central tendency, with the median

shown with a vertical line dividing the box into two. Additionally, astar or asterix is placedat the

mean value, centred inthe box in the vertical direction. The whiskers which extend to the sidesreach

the minimum and maximum values.