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2. Mean - ungrouped frequency distribution

The mean of the ungrouped frequency distribution can be determined using the formula:

$\overline X = \frac{f_1 x_1 + f_2 x_2 + ... + f_n x_n}{f_1 + f_2 + ... + f_n}$

$= \frac{\sum_{i=1}^{n} f_i x_i}{\sum_{i=1}^{n} f_i}$

Example:

The height(in

$cm$ ) of

$20$ students in a classroom are:

Find the mean height of the

$20$ students.

Solution:

To find the value of

$f_ix_i$ , multiply the value of

$x$ and

$f$ of each entry.

Consider for the mark

$130$ . That is,

$130 \times 1 = 130$

Similarly, for the mark

$135$ , we have

$135 \times 2 = 270$ and so on.

Tabulating these values, we get:

Substituting the known values in the above formula, we get:

Mean

$\overline X = \frac{3032}{20}$

$= 151.6$

Therefore, the mean of the given data is

$151.6$ .

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