Question

If the mean of 3, 4, x, 7, 10 is 6, then find the value of x.
A. \[4\]
B. \[5\]
C. \[6\]
D. \[7\]

Answer 1

Hint:In order to solve the question, first write the formula to find the mean. Next, substitute the given values. Finally, cross multiply and find the required value.

Formula Used:
\[{\rm{Mean}} = \dfrac{{{\rm{Sum\, of\, observations}}}}{{{\rm{Number\, of \,observations}}}}\]

Complete step by step solution:
Given that
The mean is 6.
We know that
\[{\rm{Mean}} = \dfrac{{{\rm{Sum\, of \,observations}}}}{{{\rm{Number\, of \,observations}}}}\]
That is
\[{\rm{Mean}} = \dfrac{{{\rm{3 + 4 + x + 7 + 10}}}}{{\rm{5}}}\]
          \[6 = \dfrac{{{\rm{3 + 4 + x + 7 + 10}}}}{{\rm{5}}}\]
   \[{\rm{24 + x}} = {\rm{6}} \times {\rm{5}}\]
            \[x = 30 - 24\]
            \[x = 6\]

Hence the correct option is C.

Additional information:
The mean is the same as the average. The sum of all data divided by the number of data gives the average or mean of the observations.
The mean of data is usually denoted by x̄.
We can find the mean of data if it contains two or more observations.
There are three types of the mean.
Arithmetic mean: The sum of observations is divided by the number of observations.
Geometric mean: The nth square root of the product of the first n geometric terms.
Harmonic mean: The reciprocal of the arithmetic mean of the harmonic term.

Note: Students can get confused about whether they need to count the term x while writing the number of observations. Here the number of observations will be 5 and not 4. Also, remember that both mean and arithmetic mean are the same.