Univariate Data

NZ Level 5

Mode

Lesson

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 **mo**st **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!

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

Mode = $\editable{}$

Find the mode from the histogram shown.

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.

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.

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