Question

Find the mode of the following sets of the numbers: 9, 0, 2, 8, 5, 3, 5, 4, 1, 5, 2, 7

Answer 1

Hint: Here, we have to find the mode of the given data set. Now, mode is the number that occurs most frequently in the given data set. That means to find the mode of the given data set, we need to find out which number is occurring the most number of times in the given data set.

Complete step by step solution:
In this question, we are given a set of 12 numbers and we need to find its mode.
Given numbers: 9, 0, 2, 8, 5, 3, 5, 4, 1, 5, 2, 7
Now, first of all, let us see what mode is.
Mode is the one of the three measures of central tendency. The other two are Median and Mean.
Mean is the average of the given numbers, median is the middle number between the given numbers and the mode is the number that occurs the most number of times in the data set.
That means, to find the mode of the given numbers, we need to find the number that occurs the most in the given data set. Let us see the occurrence of each number in this data set.
0 – 1 time
1 – 1 time
2 – 2 time
3 – 1 time
4 – 1 time
5 – 3 times
7 – 1 time
8 – 1 time
9 – 1 time
Here, we can see that 5 occurs 3 times which is the most number of times in the given data set. Hence, we can conclude that the mode of the given numbers is 5.
Note that there can be more than 1 mode of a given data set.
So, the correct answer is “5”.

Note: Here, we can also find the mean and the median of the given data set.
Mean is the average of the numbers, so it can be given by adding all the numbers and dividing by total number of numbers.
\[
   \Rightarrow Mean\left( {\overline x } \right) = \dfrac{{\sum x }}{n} \\
   \Rightarrow Mean\left( {\overline x } \right) = \dfrac{{9 + 0 + 2 + 8 + 5 + 3 + 5 + 4 + 1 + 5 + 2 + 7}}{{12}} \\
   \Rightarrow Mean\left( {\overline x } \right) = \dfrac{{51}}{{12}} \\
   \Rightarrow Mean\left( {\overline x } \right) = 4.25 \;
 \]
Now, median is the middle number between the given numbers. The median of a given data set if total number of numbers is even is given by
$
   \Rightarrow Median = \dfrac{{{{\left( {\dfrac{n}{2}} \right)}^{th}}observation + {{\left( {\dfrac{n}{2} + 1} \right)}^{th}}observation}}{2} \\
   \Rightarrow Median = \dfrac{{{6^{th}}observation + {7^{th}}observation}}{2} \\
   \Rightarrow Median = \dfrac{{3 + 5}}{2} \\
   \Rightarrow Median = \dfrac{8}{2} \\
   \Rightarrow Median = 4 \;
 $