Question

What is the mean, median, and mode for \[1,2,1,2,1,3,3,4,3\]?

Answer 1

Hint: To solve the question, we will first arrange the numbers in order from lowest to highest. Then we will calculate the Mean by dividing the sum of the numbers by the total number of numbers. Median is the middle number. Mode is the number that appears the maximum number of times.

Complete step by step answer:
First, we will arrange the numbers in order from the lowest number to the highest. So, we have; \[1,1,1,2,2,3,3,3,4\]. Now we know that the mean is like the average i.e., sum of the numbers divided by the total number.
\[\text{Mean} = \dfrac{{{\text{sum of the numbers}}}}{{{\text{total numbers}}}}\]

We have the total numbers equal to \[9\].
So, putting the value we get;
\[\text{Mean} = \dfrac{{1 + 1 + 1 + 2 + 2 + 3 + 3 + 3 + 4}}{9}\]
\[\Rightarrow \text{Mean} = \dfrac{{20}}{9}\]
\[\Rightarrow \text{Mean} = 2.22\]

Hence the mean is \[2.22\].

Now when there are a total of nine numbers, the middle number will be the fifth number.Hence the median will be the fifth number.
\[1,1,1,2,2,3,3,3,4\]
We can see that the fifth number is \[2\].

So, the median will be \[2\].

Now, we know that the mode is the number that occurs the maximum number of times. So, in the numbers given we can see that both \[1,3\] occurs three times.

So, the given data has two modes \[1,3\].

Note: One thing we should note is that when we write the median, we select the middle number. But we should be careful here that while selecting the middle number the numbers should be arranged properly. If we select the numbers from the unordered number, as given in the question, then we will get an incorrect answer.