Question

If the mode of the following distribution is $2.8$, then find the value of x.
\[2.5,2.8,2.5,2.5,2.1,2.7,2.8,2.5,x,2.8,2.8,2.7\]

Answer 1

Hint: The observation with the highest frequency is called mode of data or distribution. Mode is the value that appears most number of times.

Complete step by step answer:
\[2.5,2.8,2.5,2.5,2.1,2.7,2.8,2.5, x, 2.8,2.8,2.7\]
It is given that mode of this distribution is $2.8$,
First arrange the given number in ascending order and put unknown value x anywhere,
$2.1,2.5,2.5,2.5,2.7,2.7,2.8,2.8,2.8$,x
$2.5-3$Times
$2.8-3$Times
We can see $2.5$ is repeating three times and $2.8$ also does so, but we have given that mode of the distribution is $2.8$
As we know that mode is defined as the value of higher frequency in a given set and, in this question, this will only happen when $x=2.8$.

So, the correct answer is “2.8”.

Note: If any distribution has one mode then it is called unimodal but It may happen that in a distribution more than one data or numbers have the same frequency, in this case these all numbers are called mode of the distribution.
Having two modes is called- bimodal
For example let A = $2,3,6,2,6,4,6,2$ mode of set A are $2$ and $6$ because $2$ and $6$ have the same frequency.
Having three modes is called- trimodal
For example let A = $2,5,6,4,6,6,5,2$ mode of set A are $2$, $5$ and $6$ because $2$, $5$ and $6$ have the same frequency.
Having four or mores mode is called- multimodal
Mode = most often data