Question

Find the mode of the following data. \[12,24,36,46,25,38,72,36,25,38,12,24,46,25,12,24,46,25,72,12,24,36,25,38\] and \[36\].

Answer 1

Hint: Mode of a set of data means the value which appears the most often. To find the mode in the given data we will first arrange it in the form of a table and note down the total different values and their frequencies. Out of these, the value which has the highest frequency will be the mode of the given set of data.

Complete step-by-step answer:
Out of the given set of numbers, there are only \[7\] different values which are repeated again and again. These values are \[12,24,25,36,38,46\] and \[72\].
We will represent the frequencies of these values in the table below to help solve easily. Also we will arrange these values in ascending order to further ease the question.
The frequency of each value is found out by counting the number of times a particular value has been repeated.

Value	\[12\]	\[24\]	\[25\]	\[36\]	\[38\]	\[46\]	\[72\]
Frequency	\[4\]	\[4\]	\[5\]	\[4\]	\[3\]	\[3\]	\[2\]

Now, by observing the frequencies of all the values we can say that the number \[25\] is repeated a maximum number of times at \[5\], whereas \[72\] is repeated a minimum number of times at \[2\] times.
Thus, by the definition of mode, the number having maximum frequency, here it is \[25\], is the mode of the set of data.
Thus, the mode of the given set of data will be \[25\].

Note: Finding mode in a set of data helps in predicting the approximate mean of a set of data. The mean of a data will be closer to the number that is repeated maximum number of times, which by definition is the mode of the set of data.