Question

Average of 9 numbers is 14. If one number 12 is excluded, find the new average.

Answer 1

Hint: Observe what all is given in the question and what information can be extracted from the question to help solve the problem. Keep in mind the basic formula of average.

Complete step by step answer:
For a given set of values , there exists a central value which is known as the average value for that set of values.
Mathematically, it is defined as the ratio of summation of all the data to the number of units present in the list.
Average=${\displaystyle \frac{Sum}{No.ofvalues}}$
Finding average is very useful in real-life. Average gives us an overall picture of the data set .
It takes into account every value in the data set and therefore is considered the most accurate.
Steps to solve the problem include:
Firstly we have a look at what we are given.
The average value and the number of values are given.
Next we focus on what we can interpret from the given information.
We can find the sum of values from the given information by applying the average formula.
Let us assume that the sum of nine numbers is $x$.
Therefore, according to the formula, we have
${\displaystyle \frac{x}{9}}=14$
On solving this, we get $x=126$
Now we look into what according to the question we have to find.
We have to find the new average value if 12 is removed from the set of values .
New Average=${\displaystyle \frac{newSum}{newNum}}$
We already have the sum of the initial set of values which is 126.
We will have to subtract 12 from the initial sum to obtain the new sum of values .
Now if $12$ is excluded, sum=$126-12=114$
After removing 12, the number of values left are 9-1=8.
We again apply the average formula and calculate the new average.
So the new average now becomes,
New Average=${\displaystyle \frac{114}{8}}=14.25$
Hence the new average is 14.25.

Note: Note that the number of values will also decrease when a value is excluded. Usually we forget to decrease the number of values and only subtract from the sum. To save time and solve the problem faster, always remember that , Increase in average=(old average-quantity left)/no. of items excluding the item that left.