Formula

Mean of a frequency distribution

Statistics • Mean

Formula

x ˉ = \frac{\sum f _{i} x _{i}}{\sum f _{i}}

For values

x_{i}

with frequencies

f_{i}

x ˉ = \frac{\sum f _{i} x _{i}}{\sum f _{i}}

. For grouped data,

x_{i}

is the class midpoint.

How to use it

1For grouped data take $x_{i}$ as the midpoint of each class.
2If the mean is given and one frequency is unknown, set up the equation and solve for it.
3 $\sum f_{i}$ is the total number of observations, not the number of classes.

Find the mean of

x = 10, 20, 30

with frequencies

2, 3, 5

Step-by-step

1
$\sum f_{i} x_{i} = 20 + 60 + 150 = 230$
Why: Multiply each value by its frequency.
2
$\sum f_{i} = 10$
3
$x ˉ = \frac{230}{10} = 23$

Answer

23

Watch out

Dividing by the number of CLASSES instead of

\sum f_{i}

is the standard error.

Also known as

weighted mean, average of grouped data, assumed mean