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# To examine ungrouped numerical data to determine the mode and the median

Module by: Siyavula Uploaders. E-mail the author

## Memorandum

1. 1.1 45

• 45
• 41,5

2. 2.1 18 / 13

• 6

3. 3.1 17 / 19

• 38

4. 4.1 5,5

• 13,7

5. 5.1 Class / Subject

## Content

### ACTIVITY: To examine ungrouped numerical data to determine the mode and the median [LO 5.5]

By this time you will have realised that data can be represented in numerous ways. Let us see how data can be used within the school situation:

Mr Marvin’s class has written a Mathematics test for a total of 50 marks and the boys' results are as follows:

47 ; 33 ; 45 ; 49 ; 38 ; 45 ; 42 ; 45 ; 30

Instead of representing the data by means of a graph, Mr Marvin has calculated the mode, median and arithmetical average.

DID YOU KNOW?

The mode of the data is the value that appears most often.

Sometimes there is more than one mode.

The median of the data is the value in the middle when the data is

arranged from small to big.

If there is an equal number of values, the median is the average of the two

middle numbers.

The arithmetical average is what you get when all the values are added

together and divided by the number of values.

1. Let us help Mr Marvin calculate the following:

1.1 The mode:

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

1.2 The median:

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

1.3 The arithmetical average:

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

2. Determine the mode of:

2.1 18 ; 13 ; 15 ; 18 ; 19 ; 12 ; 13 ; 14

2.2 5 ; 6 ; 6 ; 7 ; 9 ; 8 ; 7 ; 6 ; 8 ; 9

3. Determine the median of:

3.1 17 ; 15 ; 23 ; 15 ; 19 ; 29

3.2 41 ; 29 ; 50 ; 33 ; 45 ; 27 ; 38

4. Determine the arithmetical average of:

4.1 5 ; 7 ; 8 ; 3 ; 4 ; 9 ; 2 ; 6

4.2 11 ; 14 ; 16 ; 12 ; 13 ; 15 ; 15

5.1 What arithmetical average does your educator determine regularly?

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

5.2 Why?

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

## 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 5.5: We know this when the learner examines ungrouped numerical data to determine the most frequently occurring score (mode) and the midpoint (median) of the data set in order to describe central tendencies.

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