Question

Find the mode of the following data.
1) $74,81,62,58,77,74$
2) $43,36,27,25,36,66,20,25$
3) $55,51,62,71,50,32$
4) $24,20,27,32,20,28,20$

Answer 1

Hint: First we have to know about mode. The definition of the mode is that, in the statistics part, the mode is a value which occurs most of the time in a given set of data values, or the value that appears maximum number of times, or it is a value which repeats more often or most recurring value in the given set of data. Mode is the value of the variable of which the frequency is maximum.

Complete step-by-step solution:
We know that the mode is a statistical value which repeats in a given set of observations for a maximum number of times.
Here let us take each observation at a time and count how many times that particular observation has occurred.
1) Let us find the mode of $74,81,62,58,77,74$
No. of times 74 got occurred: 2 times
No. of times 81 got occurred : 1 time
No. of times 62 got occurred : 1 time
No. of times 58 got occurred : 1 time
No. of times 77 got occurred : 1 time
As 74 occurs for a maximum number of times.
$\therefore $Mode is 74.
2) Let us find the mode of $43,36,27,25,36,66,20,25$
No. of times 43 occurred : 1 time
No. of times 36 occurred : 2 times
No. of times 27 got occurred : 1 time
No. of times 25 got occurred : 2 times
No. of times 66 got occurred : 1 time
No. of times 20 got occurred : 1 time
As 25 and 36 occurred for a maximum number of times.
$\therefore $Mode is 25 and 36.
3) Let us find the mode of $55,51,62,71,50,32$
No. of times 55 occurred : 1 time
No. of times 51 occurred : 1 time
No. of times 62 occurred : 1 time
No. of times 71 occurred : 1 time
No. of times 50 occurred : 1 time
No. of times 32 occurred : 1 time
Here all the observations occurred only once.
$\therefore $There is no mode in these observations.
4) Let us find the mode of $24,20,27,32,20,28,20$
No. of times 24 occurred : 1 time
No. of times 20 occurred : 3 times
No. of times 27 occurred : 1 time
No. of times 32 occurred : 1 time
No. of times 28 occurred : 1 time
Here 20 occurred for a maximum number of times.
$\therefore $Mode is 20.

Note: While finding the mode of any data we have to carefully observe at each observations in order to check how many times it has occurred, and in the given set of observations, if there is no observation that has not occurred at least more than once or if all the observations have occurred as the same number of times as the rest of the observations then there is no mode to such kind of data.