Univariate Data

Lesson

The range is a measure of **spread** in a quantitative (numerical) data set. In other words, it describes whether the scores in a data set are very similar and clustered together, or whether there is a lot of variation in the scores and they are very spread out.

If we looked at the range of ages of students in Year $7$7, everyone would be between $11$11 and $14$14, so the range is $3$3 ($14-11$14−11). This is quite a small range.

However, if we looked at the ages of people waiting at a bus stop, the youngest person might be a $2$2 year old and the oldest person might be a $90$90 year old. The range in this set of data is $88$88 ($90-2$90−2) which is quite a large range.

To calculate the range

Subtract the lowest score in the set from the highest score in the set.

Find the range of the following set of scores:

$10,7,2,14,13,15,11,4$10,7,2,14,13,15,11,4

The range of a set of scores is $8$8, and the highest score is $19$19.

What is the lowest score in the set?

In a study, a group of people were shown $30$30 names, and after $1$1 minute they were asked to recite as many names by memory as possible. The results are presented in the dot plot.

Each dot represents:

One person in the group

AOne name remembered

BOne person in the group

AOne name remembered

BHow many people took part in the study?

What is the largest number of names someone remembered?

What was the smallest number of names someone remembered?

What is the range?

Remember, the range only changes if the highest or lowest score is changed. Otherwise it will remain the same.

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 range be affected?

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

Do:

The range when the score was an $8$8 was $8$8 ($9-1$9−1). The range when the score was changed to a $9$9 was also $8$8 ($9-1$9−1). Since the score that was changed was not the highest or the lowest score, the range did not change.

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