Question

What is the mean of the following data?
$45,35,20,30,15,25,40$

Answer 1

Hint: Mean is also called the average and the mean of $n$ numbers which are ${x_1},{x_2},{x_3},...........,{x_n}$ is $\dfrac{{\sum {{x_i}} }}{n}$
Therefore we say that ${\text{mean}} = $$\dfrac{{\sum {{x_i}} }}{n}$ where $\sum {{x_i}} $is the sum of all the values of the data given and $n$ is the number of items that is frequency given.

Complete step-by-step answer:
So basically mean or the arithmetic mean is the average of the numbers given. So if we have $n$ numbers which are ${x_1},{x_2},{x_3},...........,{x_n}$ then their mean is the ratio of the sum of all the numbers and the total numbers of items or the frequency of the setoff all the observations.
For example the mean of the two numbers like $2,6$ is $\dfrac{{2 + 6}}{2} = \dfrac{8}{2} = 4$
Hence as here we have two terms so we divide by two and we have two numbers so we have done their sum in the numerator.
Again if we have three numbers like $3,4,5$ then again now we have three terms so we will divide by three and the sum will be there in the numerator so we can write the formula now as
${\text{mean}} = \dfrac{{3 + 4 + 5}}{3} = 4$
Similarly now here we have $7$ numbers so here again the sum of all the numbers will be in the numerator and the total number of terms which are $7$ will be in the denominator.
$\sum {{x_i}} = 45 + 35 + 20 + 30 + 15 + 25 + 40 = 210$
$n = 7$
Now we know that ${\text{mean}} = $$\dfrac{{\sum {{x_i}} }}{n}$
Mean$ = \dfrac{{210}}{7} = 30$
Hence we get that mean of these given numbers is $30$.

Note: We know that if we have the value of the mean and the median then we can find the mode by the following formula which is
${\text{mode}} = 3{\text{median}} - 2{\text{mean}}$