4.14 Modes, medians and arithmetic mean

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Activity: modes, medians and arithmetic mean [lo 5.6, lo 5.9]

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.

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

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

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

Assessment

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.

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