Direct method — lesson. Mathematics CBSE, Class 10.

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The formula for finding the arithmetic mean using the direct method is given by:

$\overline X = \frac{\sum f_ix_i}{\sum f_i}$

Where

$i$ varies from

$1$ to

$n$ ,

$x_i$ is the midpoint of the class interval and

$f_i$ is the frequency.

Steps:

1. Calculate the midpoint of the class interval and name it as

$x_i$ .

2. Multiply the midpoints

$x_i$ with the frequency

$f_i$ of each class interval and name it as

$f_ix_i$ .

3. Find the values

$\sum f_ix_i$ and

$\sum f_i$ .

4. Divide

$\sum f_ix_i$ by

$\sum f_i$ to determine the mean of the data.

Example:

The following frequency distribution table shows that the number of trees based on the height in metres. Find the average height of the trees.

Height (in $m$ )	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Number of trees	$124$	$156$	$200$	$10$	$10$

Solution:

Let us form a frequency distribution table.

Mean

$\overline X = \frac{23760}{500}$

$= 47.52$

Therefore, the average height of the trees is

$47.52$ .

Did you find an error?

4. Direct method