Answer

Verified

412.2k+ views

**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.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

Which are the Top 10 Largest Countries of the World?

Write a letter to the principal requesting him to grant class 10 english CBSE

10 examples of evaporation in daily life with explanations

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE