Question

Calculate the Arithmetic mean of the following data by direct method

X	5	10	15	20	25	30
f	4	5	7	4	3	2

Answer 1

We will start with making the same table and then we will find $f(x)$ in the table. Then we are going to sum up the f and $f(x)$ then we will apply the arithmetic mean method to the table. The method we will use is the direct arithmetic method. This way we will get the answer.

Complete step by step solution:
Copy the table given in the question and then add one more column for $f(x)$ which is multiple of x.f then we will sum up the f which will give us N.

x	f	$f(x) = x.f$
5	4	20
10	5	50
15	7	105
20	4	80
25	3	75
30	2	60
Total	$N = 25$	$\sum {f(x)} = 390$

We will apply the Direct arithmetic mean formula
Direct arithmetic mean $= \dfrac{{\sum {f(x)} }}{N}$
We will put the values that we find in the above table in the formula
$\Rightarrow$ Direct arithmetic mean $= \dfrac{{390}}{{25}}$
Hence, we get the arithmetic mean
$\Rightarrow$ Direct arithmetic mean =15.6

Note:
Arithmetic mean is a commonly used average to represent data. It is obtained by simply adding all the values and dividing them by the number of items. Arithmetic mean can be a simple arithmetic mean or weighted arithmetic mean. There are many ways we can find the Arithmetic mean of the data. The types are, Direct method and shortcut method. It helps to get the data average.