Question

If the mean of 20, 24, 36, 26, 34 and $k$ is 30, then find $k$.

Answer 1

Hint: The definition of mean is given as the sum of a collection of numbers divided by the count of numbers in the collection. We are given the mean of a collection of numbers. We will compute the sum of the given collection of numbers. Then we will use the definition of mean to find the value of $k$.

Complete step-by-step answer:
We know that the definition of mean is given as the sum of a collection of numbers divided by the count of numbers in the collection. The formula for calculating the mean is given as
$mean=\dfrac{1}{n}\sum\limits_{i=1}^{n}{{{a}_{i}}}$
where $n$ is the count of the collection of numbers and ${{a}_{i}}$ are the elements in the collection of numbers.
The given collection of numbers is of 20, 24, 36, 26, 34 and $k$. Now, we will compute the sum of this collection of numbers. The sum is calculated as follows,
$sum=20+24+36+26+34+k$
Adding these numbers, we get
$sum=140+k$
Now, we know that the mean of the given collection of numbers is 30. And we know that there are 6 numbers in this collection. So, we have $n=6$ and $mean=30$. We also know that the sum of the elements in the given collection is $sum=140+k$. We will substitute these values in the formula for calculating mean as follows,
$30=\dfrac{1}{6}\times \left( 140+k \right)$
Multiplying both sides of the above equation by 6, we get
$180=140+k$
Solving the above equation for $k$, we get
$\begin{align}
  & k=180-140 \\
 & =40
\end{align}$
Therefore, the value of $k$ is 40.

Note: In this type of questions, it is important that we are familiar with the concept of mean or average. The concept of average is important since it gives us a representative value of a set of values. We should be able to use the formula we know to our advantage. It is necessary that we do the calculations in a detailed manner so that we can avoid making any errors.