Question

Find the value of x, if the mode of the following data is 25.
25,20,25,18,14,15,18,16,20,25,20,x,18

Answer 1

Hint: We here have been given a scattered data and with one of them as ‘x’ and their mode as 25 and we have to find the value of ‘x’. For this, we will first arrange the data in ascending order keeping ‘x’ at the first position. Then we will draw a frequency distribution table for all the data elements of the given data. We will then observe which data element has the highest frequency. We will observe that 3 data elements will have the same highest frequency. So, the mode will have to have a higher frequency than that and hence if we assign that value to x, we will get the required mode. As a result, we will get the required answer.

Complete step by step answer:
We know that mode of any scattered data is given as the observation with highest frequency. Here, we have been given the data stated as follows:
25,20,25,18,14,15,18,16,20,25,20,x,18
Now, arranging them in ascending order we get:
x,14,15,16,18,18,18,20,20,20,25,25,25
We have kept ‘x’ at the first position because it’s an unknown quantity and it can be seen separately ar first.
Now, if we make the frequency distribution table of this data, we get:

DATA	FREQUENCY
x	1
14	1
15	1
16	1
18	3
20	3
25	3

Now, we have been given that the mode of the data is 25.
Hence, the observation with the highest frequency is 25.
Here, the frequency of 25 is 3. But this is also the frequency of 18 and 20. Hence, for 25 to be the mode, the frequency of 25 should be at least 4.
Now, since ‘x’ is the unknown quantity here, we can assign it the value of 25 as a result of which the frequency of 25 will become 4.
Hence, we get our required value of x as 25.
Thus, \[x=25\]

Note:
We here have arranged the data in ascending order because it is easy in this order to draw a frequency distribution table. It is not a necessary step and it will also take a lot of time if the data given to us is large. Similarly, we have here drawn a frequency distribution table for a small amount of data but it is also not a necessary step, just a step that makes the working easier. But it is necessary for a large amount of data otherwise there will be a lot of confusion and hence it will result in a wrong answer.