Arithmetic mean - grouped frequency distribution — lesson. Mathematics State Board, Class 9.

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Consider the frequency distribution table.

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

The above frequency table shows that the data are grouped in class intervals. This table shows that the number of trees with various heights.

Consider the interval

$50 - 60$ . There are

$200$ trees in the heights between

$50 - 60$ metres. In grouped frequency, the individual observations are not available. Thus, we need to determine the value that indicates the particular interval. This value is called a midpoint or class mark. The midpoint can be determined using the formula:

Midpoint

$= \frac{UCL + LCL}{2}$

Where

$UCL$ is the upper class limit and

$LCL$ is the lower class limit.

Example:

Consider the interval

$40 - 50$ . Let us find the midpoint of this interval.

Here,

$UCL = 40$ and

$LCL = 50$

Midpoint of