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Mean of three numbers is 50. If two of them are 30 and 50. What is the third number?

Last updated date: 20th Jun 2024
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Hint: Here in this problem given the mean of the three numbers, and given the value of the two numbers, we are asked to find the value of the third number. To solve this problem we have to know about the arithmetic mean. Arithmetic mean is a statistical value, which is the average of the given set of data.

Complete step-by-step solution:
Arithmetic mean is the ratio of the sum of observations in the given set of data to the total number of observations. It is expressed mathematically below:
Let ${x_1},{x_2},{x_3},.....{x_n}$ be the observations of a set of data, then the mean is given by:
$ \Rightarrow \overline x = \dfrac{{\sum\limits_{i = 1}^n {{x_i}} }}{n}$
Here $\overline x $ is the mean of the given set of data.
$\sum\limits_{i = 1}^n {{x_i}} $ is the sum of the observations in the given set of data.
$n$ is the total number of observations.
Now given that the mean of three numbers is 50, given by:
Let the three numbers be ${x_1},{x_2},{x_3}$, here the total no. of observations is 3.
Also given that two of the values are 30 and 50,
$\therefore {x_1} = 30,{x_2} = 50.$
The mean of the three numbers are mathematically expressed as given below:
\[ \Rightarrow \dfrac{{{x_1} + {x_2} + {x_3}}}{3} = 50\]
\[ \Rightarrow \dfrac{{30 + 50 + {x_3}}}{3} = 50\]
\[ \Rightarrow 80 + {x_3} = 150\]
\[ \Rightarrow {x_3} = 70\]
$\therefore {x_3} = 70$

The value of the third number is 70.

Note: Here used the general arithmetic mean formula to find the value of an unknown number, given already the value of the arithmetic mean. It is always important to remember that to consider the correct number of total observations, as it plays a major role in finding the mean.