11. MODES, MEDIANS AND ARITHMETIC MEAN

11.1 LEARN the following CONCEPTS

MODE :

The value that is repeated the most often

E.g. 5; 6 ;6 ;7; 4 ; 8 ; 6 ; 6

The mode is 6.

Sometimes there is more than one mode:

E.g. 2; 3 ; 3 ; 4 ; 6; 2 ; 5

The modes are 2 and 3.

MEDIAN :

This is the value that lies in the middle when data is arranged from smallest to biggest.

E.g. 18 ; 21 ; 22 ; 23 ; 27 ; 31 ; 40

If there is an even number of values, then the median is the average of the two centre values.

E.g. 4 ; 5 ; 6 ; 6 ; 6 ; 7 ; 7 ; 9 ; 9 ; 10

The median = (7 + 6) ÷ 2 = 6,5

ARITHMETIC MEAN (AVERAGE):

Add all the values together and divide by the number of the values.

E.g. 2; 3; 5; 5; 6

= 21 ÷ 5

= 4,2

11.2 Here follows a list of the shoe sizes of ten Grade 7 boys:

6 ; 7 ; 9 ; 8 ; 8 ; 9 ; 5 ; 6 ; 7 ; 8

a) Calculate the mode: ______________________________________________

b) Calculate the median: ____________________________________________

c) If the shoe sizes were a mark out of 10, what would the arithmetic average of the “test” be?

11.3 Calculate the average age (in years) of your class.

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11.4 Choose 10 of your classmates and determine the average number of children per family.

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* Learning Outcome 5:*The learner will be able to collect, summarise, display and critically analyse data in order to draw conclusions and make predictions, and to interpret and determine chance variation.

* Assessment Standard 5.6:*We know this when the learner identifies the largest and smallest scores in a data set and determines the difference between them in order to determine the spread of the data (range);

* Assessment Standard 5.9:*We know this when the learner summarises ungrouped numerical data by determining mean, median and mode as measures of central tendency and distinguishes between them.