Question

Find the mode of 10, 12, 11, 10, 15, 20, 19, 21, 11, 9, 10.

Answer 1

Hint: First understand the meaning of ‘mode’ for a given set of values. Now, to find the mode of the given data find the number which is appearing the most number of times. Draw a table of two columns in which consider the different values, in the given data set, in the first column and consider the number of times it is appearing in the second column.

Complete step by step solution:
Here, we have been provided with the data set 10, 12, 11, 10, 15, 20, 19, 21, 11, 9, 10 and we have been asked to determine the mode of this data set. But first we need to know that meaning of the term ‘mode’.
Now, in statistics, the mode of a given data set is the value that appears most often or in other words the value that appears most number of times. The mode is the value at which the probability mass function takes its maximum value. It is the value that is most likely to be sampled. The numerical value of the mode is the same as that of a mean and median in a normal distribution.
Let us come to the question. We have the given data set, so let us draw a table containing two columns where in the first column we will mention the numbers given in the data set and in the second column we will mention the number of times they are appearing. So, we have,

Data values	Number of times appearing
9	1
10	3
11	2
12	1
15	1
19	1
20	1
21	1

From the above table we can see that the data 10 is occurring the most number of times, i.e., 3 times. So, we can say that the mode of the given data set is 10.
Hence, 10 is our answer.

Note: One may note that here we have obtained only one for the given data set so the given data set is referred to as unimodal. Remember that if two values in the data set will appear the same and maximum number of times then the data set will have two modes and the data set will be called bimodal. If there will be more than two modes then the data set will be called multimodal. Remember that for a normal distribution the mean, median and mode values coincide. You must remember the meanings of mean and median also because they will be used frequently in the topic ‘statistics.