Question

Check whether the mean and median of the first five odd numbers are equal or not?

Answer 1

Hint: This type of problem is based on the concept of mean and median. First, we have to find the first five odd numbers. we get that the first five odd numbers are 1, 3, 5, 7 and 9. According to the definition of mean, we have to sum all the considered number and divide it by the total number of odd numbers considered. Here, the sum is 1+3+5+7+9 and the total number of odd numbers considered is 5. We get \[\dfrac{1+3+5+7+9}{5}\]. Do necessary calculations and find the mean. Now, we have to find the median. According to the definition, median is the \[\dfrac{n}{2}\]th term if n is even and is \[\left( \dfrac{n+1}{2} \right)\]th term when n is odd and n is the number of terms considered. Here, n is equal to 5 which is an odd number, so we have to consider \[\left( \dfrac{n+1}{2} \right)\]th term. Substitute the value of n and do necessary calculations and find the median in the first five odd numbers.

Complete step-by-step answer:
According to the question, we are asked to find the mean and median of the first five odd numbers.
We have to find the first five odd numbers.
According to the definition of odd numbers, they are not divisible by 2.
Here, we find that 1, 3, 5, 7, 9, 11… are odd numbers.
But we are asked for the first five odd numbers.
Therefore, the first five odd numbers are 1, 3, 5, 7 and 9.
Let us now find the mean.
We know that mean is equal to the sum of considered term divided by the total number of terms.
That is, \[mean=\dfrac{\text{sum of the terms}}{\text{total number of terms}}\].
Here, we have considered five odd numbers.
Therefore, total number of terms will be equal to 5.
The sum of first five odd numbers is 1+3+5+7+9.
\[\Rightarrow 1+3+5+7+9=4+5+7+9\]
On further simplification, we get
1+3+5+7+9=9+7+9
\[\Rightarrow 1+3+5+7+9=18+7\]
\[\therefore 1+3+5+7+9=25\]
Therefore, the sum of the terms is equal to 25.
Now, let us substitute the values in the formula for mean.
\[\Rightarrow mean=\dfrac{25}{5}\]
On cancelling the common term 5 from the numerator and denominator, we get
Mean=5
Therefore, the mean of the first five odd numbers is equal to 5.
Now, we have to find the median of the terms 1, 3, 5, 7 and 9.
According to the formula to find the median, if the total number of terms ‘n’ is equal to an odd number, then \[\left( \dfrac{n+1}{2} \right)\]th term is the median.
Add if ‘n’ is an even number, then \[\left( \dfrac{n}{2} \right)\]th term is the median.
Here, n=5 and we know that 5 is an odd number.
Therefore, we have to use the formula \[\left( \dfrac{n+1}{2} \right)\].
On substituting the value of n, we get
\[\dfrac{n+1}{2}=\dfrac{5+1}{2}\]
On further simplification, we get
\[\dfrac{n+1}{2}=\dfrac{6}{2}\]
On cancelling the common term 2 from the numerator and denominator, we get
\[\dfrac{n+1}{2}=3\]
So, we get that the 3rd term from the considered number is the mean.
The considered numbers are 1, 3, 5, 7 and 9.
Here, the third term is 5.
Therefore, the median of the first five odd numbers is 5.
Hence, the mean and median of the first five odd numbers are the same which is equal to 5.

Note: We should not get confused by mean, median and mode. To find the median, we have to use the formula for odd terms in this condition. If not, we get the wrong answer. Do the calculations correctly so that we get the correct mean.