Mode
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 $$10 people how many pets they had and $$2 people said no pets, $$6 people had one pet and $$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 $$610 had one pet. So the mode in this data set is $$1.
Mode = Most
Worked Examples
Question 1
Find the mode of the following scores:
$$8,18,5,2,2,10,8,5,14,14,8,8,10,18,14,5
Mode = $$
Question 2
Find the mode from the histogram shown.
A bar histogram titled "Histogram" displays the frequencies of various scores on the x-axis labeled "Scores", and the y-axis labeled "Frequency". The x-axis includes score labels: $$68,69,70,71,72. The y-axis is marked in increments of $$5, ranging from $$0 to $$30. The frequency list as $$14,12,18,24,13
Five bars represent the scores:
The bar for score $$68 reaches a frequency of $$14.
The bar for score $$69 reaches a frequency of $$12.
The bar for score $$70 reaches a frequency of $$18.
The bar for score $$71 reaches the highest frequency of $$24.
The bar for score $$72 reaches a frequency of $$13.
How do scores affect mode?
The mode is the most common score. So if we add or subtract a score, the mode may, but does not always, change. We just need to check which score occurs most often if the data set changes.
Example
Question 3
Assess how various changes to data sets alter their characteristics.
a. Consider the set of data: $$1,2,2,4,4,5,6,6,8,9
If the score of $$8 is changed to a $$9, how would the mode be affected?
Think: What was the mode when the score was an $$8? What was the mode when the score was changed to a $$9?
Do:
The mode when the score was an $$8 was $$2, $$4 and $$6 as all these scores occur twice. The mode changed when the score was changed to a $$9 as now $$2, $$4, $$6 and $$9 all occur twice.