Question

The marks obtained by 10 students in a test are 15, 75, 33, 67, 76, 54, 39, 12, 78, 11. Find the arithmetic mean.

Answer 1

First of all we will write the formula for the arithmetic mean. Now, the formula will require the number of observations and the sum of observations which we will calculate and put in it and thus get the answer.

Complete step-by-step answer:
We know that the formula for arithmetic mean is given by the sum of all the observations given to us divided by the number of observations that we have just summed up.
$\therefore A.M. = \dfrac{{Sum}}{{Frequency}}$, where A. M. stands for arithmetic mean.
Now, we see that we have the marks obtained by $10$ students given by $15, 75, 33, 67, 76, 54, 39, 12, 78, 11.$
Therefore, the frequency that is the number of observations is given by 10.
Now, we are just left to find the sum of all the observations.
$\Rightarrow$ Sum of observations = $15 + 75 + 33 + 67 + 76 + 54 + 39 + 12 + 78 + 11.$
Solving the RHS, we will get:-
$\Rightarrow$ Sum of observations = $460$
Now, putting these values in the formula given by $A.M. = \dfrac{{Sum}}{{Frequency}}$, we will get:-
$\Rightarrow A.M. = \dfrac{{460}}{{10}}$
Solving the RHS, we will get:-
$\Rightarrow A.M. = 46$

$\therefore$ The answer is 46.

Note: The students must know what the term “ arithmetic mean” represents. It is the simplest and widely used term in the field of “Statistics”. The word “arithmetic mean” represents the same thing as line mean only. We use it to report the central tendencies. This defines the average of all the data.
Like in the given question above, if we picked out a random kid, he would have got the average marks as 46. So, basically this 46 tells us where the marks of students mostly lie.
Arithmetic mean is given by the sum of all the observations divided by the number of observations.