NZ Level 5
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Mode
Lesson

Mode

The mode is a measure of central tendency. In other words, it's one way of describing a value that represents the middle or the centre of a data set so we get a sense of what is "normal." The mode describes the most frequently occurring score. Remember the word and the meaning start with the same two letters.

Let's say I asked $10$10 people how many pets they had and $2$2 people said no pets, $6$6 people had one pet and $2$2 people said they had two pets. What is the most common number of pets for people to have? The answer is one pet because the majority of people $\frac{6}{10}$610 had one pet. So the mode in this data set is $1$1

Remember!

Mode = Most

 

Worked Examples

Question 1

Find the mode of the following scores:

$8,18,5,2,2,10,8,5,14,14,8,8,10,18,14,5$8,18,5,2,2,10,8,5,14,14,8,8,10,18,14,5

  1. Mode = $\editable{}$

Question 2

Find the mode from the histogram shown.

HistogramScoresFrequency510152025306869707172

How do scores affect mode?

The mode is the most common score. So if we add or subtract a score, the mode may, but does not always, change. We just need to check which score occurs most often if the data set changes.

Example

Question 3

Assess how various changes to data sets alter their characteristics.

a. Consider the set of data: $1,2,2,4,4,5,6,6,8,9$1,2,2,4,4,5,6,6,8,9

If the score of $8$8 is changed to a $9$9, how would the mode be affected?

Think: What was the mode when the score was an $8$8? What was the mode when the score was changed to a $9$9?

Do:

The mode when the score was an $8$8 was $2$2, $4$4 and $6$6 as all these scores occur twice. The mode changed when the score was changed to a $9$9 as now $2$2, $4$4$6$6 and $9$9 all occur twice.

 

Outcomes

S5-1

Plan and conduct surveys and experiments using the statistical enquiry cycle:– determining appropriate variables and measures;– considering sources of variation;– gathering and cleaning data;– using multiple displays, and re-categorising data to find patterns, variations, relationships, and trends in multivariate data sets;– comparing sample distributions visually, using measures of centre, spread, and proportion;– presenting a report of findings

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