Question

Find the mode of 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18.

Answer 1

Hint: We will first arrange all the data in the ascending order. After doing that, we will count how many times one number occurs in this data. So, the maximum number of times if any data is appearing, it will be the mode of the data.

Complete step-by-step answer:
We are given the following data: 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18
We see that we have a total of 12 numbers with us.
Among this, 14 is the smallest, then comes 17, then 18, then 22, then 23, then 25 and then 28.
So, we will first have to write 14, 14, 14, 14.
Now, we have covered 4 observations out of 12.
Next we will write 17’s which is given only once in the data.
So, after 17, we are left with 7 observations.
Next we will write 18’s which is given thrice in the data.
So, after 18, we are left with 4 observations.
Next we will write 22’s which is given only once in the data.
So, after 22, we are left with 3 observations.
Next we will write 23’s which is given only once in the data.
So, after 23, we are left with 2 observations.
Next we will write 25’s which is given only once in the data.
So, after 25, we are left with 1 observation.
Next we will write 28’s which is given only once in the data.
So, after 28, we are left with 0 observations.
Now, writing all the data together, we have: 14, 14, 14, 14, 17, 18, 18, 18, 22, 23, 25, 28.
We see that only 14 are occurring 4 times in the data.
Therefore, the mode of the given data 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18 is 14.

\[\therefore \] The mode of the given data is 14.

Note: The students must know the meaning of mode in statistics and what is the significance of finding it.
Mode is the number which appears the most number of times in a set of values.
But sometimes, it is possible to have more than 1 number the same number of times which is the highest frequency. For example, if we had one more 18 in the above data. We would have had 14 and 18 4 times in the arrangement, then, we would have had two modes and our data would be called “bimodal’. Similarly, if we have more than 2 modes, we call the data “multimodal”.
Its significance: The mode is the point where the peak of the distribution lies, that is where most samples concentrate is known as mode. So, if we are given a mode, we know what thing is happening most frequently.