Question

Determine the mode(s) of the following data set.

$23$	$47$	$74$	$54$	$63$
$47$	$91$	$87$	$27$	$74$
$54$	$26$	$84$	$19$	$49$

• A. $47$ and $87$
• B. $54$ and $91$
• C. $47$, $54$ and $74$

Answer 1

The correct option is C $47$, $54$ and $74$

First, we arrange the given data set in ascending order.

19	23	26	27	47
47	49	54	54	63
74	74	84	87	91

Frequency table of the given data set is as follows: Frequency Table

Number	Frequency	Number	Frequency
$19$	$1$	$\underset{–}{54}$	$\underset{–}{2}$
$23$	$1$	$63$	$1$
$26$	$1$	$\underset{–}{74}$	$\underset{–}{2}$
$27$	$1$	$84$	$1$
$\underset{–}{47}$	$\underset{–}{2}$	$87$	$1$
$49$	$1$	$91$	$1$

From the above frequency table, we observe that the numbers $47$, $54$ and $74$ occur $2$ times each, and $2$ is the maximum number of occurrence.

$\therefore$ The modes of the given data are $47$, $54$ and $74$.

As the given data set has three modes, it is a $\text{trimodal data}$.