Question

How do you find the mean of a data set $10$, $0$, $2$ and $8$ ?

Answer 1

Hint: To solve this question we need to know the concept of mean. Mean refers to the average of all the numbers in a set. The formula used to find the mean of the number is \[\text{mean = }\dfrac{\text{Sum of all the observations in the data set}}{\text{Total number of observations}}\]. On putting the values in the formula we get the mean for the numbers in a set.

Complete step-by-step solution:
The question asks us to find the value of Mean for the numbers $10$, $0$, $2$ and $8$ which are given in the data set. Mean for a set of numbers is defined as the average of that set of that number present in a particular set. The formula for the mean or the average is the ratio of the sum of all of the items present into the data set to the number of items present. Mathematically it will be written as :
\[\text{mean = }\dfrac{\text{Sum of all the observations in the data set}}{\text{Total number of observations}}\]
To find the mean for the given data set numbers, the first step is to find the sum of all the items present in the set so the numbers given in the data set are therefore on adding the terms $10$, $0$, $2$and $8$, we get:
$\Rightarrow 10+0+2+8=20$
So the sum of all the numbers in the data set is $20$.
Now the second step of our, will be to find the number of items present in a data set. On seeing the question we get $4$, as the total number of observations. On applying the above formula and substituting the values we get:
\[\Rightarrow \text{mean = }\dfrac{\text{Sum of all the observations in the data set}}{\text{Total number of observations}}\]
$\Rightarrow \text{mean = }\dfrac{20}{4}$
On dividing the numerator, $20$ with the denominator as $4$ we get:
\[\Rightarrow \text{mean = 5}\]
$\therefore $ The mean of the data set of $10$, $0$, $2$and $8$ is $5$.

Note: In this question $0$ is present as one of the numbers in the set, so while counting the total number of observations we will also count $0$ as one the number. We can check whether the value of mean is correct or not. For this we will have to multiply the mean with the total number of observations, if the answer comes out the same as the sum of the number given in the set then the answer we got is correct. So on solving we get:
$\text{Mean }\!\!\times\!\!\text{ No}\text{.of observations = Total sum of numbers}$
$\Rightarrow 5\times 4=10+0+2+8$
$\Rightarrow 20=20$
Since both the values are the same so the mean we got is correct.