# Recognising the centre of data

Lesson

So far we have learnt about three measures of central tendency: the mean, the median and the mode. These three measures all give us an approximation of where the centre is in a data set.

So when we are able to recognise the centre of data sets by finding the mean, median and mode, we can start to compare and make judgments about different data sets. We can say which one has the highest mode, the lowest median and so on.

#### Worked Examples

##### Question 1

For each of the following statements, decide whether they are true or false:

1. If two sets of data have the same median then the data sets must themselves be the same

True

A

False

B

True

A

False

B
2. If two sets of data have very different modes then the highest values cannot be the same

True

A

False

B

True

A

False

B

##### QUESTION 2

Select the data set from each of the options below that has:

1. The lowest mode.

$3,9,18,9,65,13$3,9,18,9,65,13

A

$5,12,16,16,86,3$5,12,16,16,86,3

B

$3,9,18,9,65,13$3,9,18,9,65,13

A

$5,12,16,16,86,3$5,12,16,16,86,3

B
2. The highest median?

$3,9,13,18$3,9,13,18

A

$9,16,16,65,86$9,16,16,65,86

B

$3,9,13,18$3,9,13,18

A

$9,16,16,65,86$9,16,16,65,86

B

##### QUESTION 3

Consider the two graphs. Select the dot plot that shows the lowest mode.

1.  ​
A
 ​
B
 ​
A
 ​
B

### 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