Question

If A.M of 1, 2, x, 3 is 0, then find the value of x?

Answer 1

Hint:
First, we will use the formula of arithmetic mean, which is often simply known as the mean, which is calculated by adding all the values and dividing it by the total number of values given.
A.M is the arithmetic mean of the given series.

Formula used:
\[Arithmetic{\text{ }}mean\;\;\; = \dfrac{{Sum{\text{ }}of{\text{ }}all{\text{ }}observation}}{{No.{\text{ }}of{\text{ }}observation}}\]

Complete step-by-step answer:
It is given that the arithmetic mean (A.M) = 0
Since there are 4 values,that are, 1, 2, x and 3. We can say that the total number of observations is 4.
$ \Rightarrow $ Total number of observations = 4
Now we are going to sum the given observations. To find the sum of the observation, we have to add the given values.
$ \Rightarrow $ Sum of all the observations = 1+2+x+3
Now we are going to substitute the sum of all the observation, total number of observation and arithmetic mean on the formula of \[Arithmetic{\text{ }}mean\;\;\; = \dfrac{{Sum{\text{ }}of{\text{ }}all{\text{ }}observation}}{{No.{\text{ }}of{\text{ }}observation}}\] $ \Rightarrow 0 = \dfrac{{1 + 2 + x + 3}}{4}$
Now we are going to add the values that are on the numerator.
$ \Rightarrow 0 = \dfrac{{6 + x}}{4}$
Now we are going to cross multiply.
$ \Rightarrow 0 \times 4 = 6 + x$
Now, on multiplying 4 with 0, we will get 0.
$ \Rightarrow 0 = 6 + x$
Now we have an equation. We are going to solve the above equation to get the value of x.
$ \Rightarrow x = - 6$
Hence the value of $x$ is -6
Additional information:
Media is the middle value of the series (when the data is arranged in any of the orders).
If the total number of observations is odd, then the median can be found by the formula of is = $\dfrac{{(n + 1)}}{2}$ , where n is the total number of observations.
If the total number of observations is even then, the median is calculated simply by taking the average of the total number of values = $\dfrac{n}{2}$ , also here n is the total number of observations.
Mode is the most common value among all the values of the series.

Note:
The formula of arithmetic mean is often denoted by
$\overline x = \dfrac{{{x_1} + {x_2} + {x_3} + ....{x_n}}}{N}$
Where $\overline x $ is the mean
${x_1}$= first value
${x_2}$= second value
And so on
${x_n}$= the last value
N = the total number of values.
If this formula is given instead of \[Arithmetic{\text{ }}mean\;\;\; = \dfrac{{Sum{\text{ }}of{\text{ }}all{\text{ }}observation}}{{No.{\text{ }}of{\text{ }}observation}}\]
Then, there is no need to get confused.