Question

Find the mode for the set of values $482,485,483,485,487,487,489$.

Answer 1

From the question, we have to find the mode of the given data. First, we have to frame a mathematical expression for the given data. Then, we have to find the mode by data handling.
The raw data will not be useful to get the required information. In order to get proper useful information, we have to arrange the data in a manner that the required information is obtained.

Formula used: We will create a frequency table to obtain the mode. The mode is the observation with the highest frequency that is the maximum number of occurrences.

Complete step-by-step solution:
Here, we first arrange the data in ascending order for the ease of understanding.
$482,483,485,485,487,487,489$
Now, we arrange the data in a frequency table with two columns- observations and frequency.

Observation	Frequency
$482$	$1$
$483$	$1$
$485$	$2$
$487$	$2$
$489$	$1$
Total	$7$

Now, mode is the observation of the data set that has the highest frequency.
So, we can say that the frequency denoted the number of occurrences for any observation.
In the given dataset, $482$ has occurred once, so, the frequency is $1$
Also, $483$ occurred once so, the frequency is $1$
Again, $485$ has occurred twice, so, the frequency is $2$ and so on.
Here, two observations have the highest frequency that is $2$ and others have frequency $1$.

Thus, these data are bimodal in nature with two modes $485$ and $487$.

Note: Mode is an essential concept in statistics. In statistics, it is a measure of central tendency of a probability distribution along median and mean. Mode helps to understand which observation has occurred most of the time. It is not affected by extreme values and is very easy to understand. It is easy to comprehend and obtain.