Question

The mode of the observation $2x+3,3x-2,4x+3,x-1,3x-1,5x+2$ (x is a positive integer) can be
A. 3
B. 5
C. 7
D. 9

Answer 1

Hint: We will use the basic definition of mode to solve this question. It states that in a given data, the most repeating term or frequency is the mode. So, we will put the smallest positive integer in place of x and find the number that is repeating the most number of times. And that number will then then be considered as the mode.

Complete step-by-step answer:
In the question, some observations, $2x+3,3x-2,4x+3,x-1,3x-1,5x+2$ (x is a positive integer) are given and we have been asked to find the mode of the given data. We know that mode is the term that has the most frequency among all the given observations, which means that mode = term having the highest frequency. We have been given that x is a positive integer and we know that the smallest positive integer is 1. So, we will put the value of x as 1 in the given data. So, we get,
$\begin{align}
  & 2x+3=\left\{ 2\left( 1 \right)+3 \right\}=5 \\
 & 3x-2=\left\{ 3\left( 1 \right)-2 \right\}=1 \\
 & 4x+3=\left\{ 4\left( 1 \right)+3 \right\}=7 \\
 & x-1=\left\{ 1-1 \right\}=0 \\
 & 3x-1=\left\{ 3\left( 1 \right)-1 \right\}=2 \\
 & 5x+2=\left\{ 5\left( 1 \right)+2 \right\}=7 \\
\end{align}$
So, we get the given observation as, 5, 1, 7, 0, 2, 7. Now, if we observe the obtained observation values, then we can see that only 7 is repeating twice and all the rest of the values appear once. This means that 7 has the maximum frequency in the given observation. Hence, we can say that the mode of the given observation is 7.
Therefore, the correct answer is option C.

Note: This is one of the most basic questions on mode in statistics, but many students make a mistake while finding the values of x, after taking its value as 1. They can make simple calculation mistakes and end up with some other values for the observation. This could lead to an incorrect answer as the answer depends on the frequency of these values. So, the students should be careful while doing simple calculations too.