This mean calculator lets you calculate the mean of a group of observations. It can also calculate for you the weighted mean if you provide the observations and the corresponding weights.

The calculator will give you not just the mean, but how to calculate it.

## Usage Guide

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#### i. Valid Inputs

Your input needs to be a list of numbers spearated by commas. Each number can be a real number in any format — integers, decimals, fractions, or even mixed numbers. Here are a few examples.

- Whole numbers or decimals → $\hspace{0.2em} 2 \hspace{0.2em}$, $\hspace{0.2em} -4.25 \hspace{0.2em}$, $\hspace{0.2em} 0 \hspace{0.2em}$, $\hspace{0.2em} 0.33 \hspace{0.2em}$
- Fractions → $\hspace{0.2em} 2/3 \hspace{0.2em}$, $\hspace{0.2em} -1/5 \hspace{0.2em}$
- Mixed numbers → $\hspace{0.2em} 5 \hspace{0.5em} 1/4 \hspace{0.2em}$

For weighted mean, weights need to be in the same order as the corresponding observations/data. Also, weights must be non-negative.

#### ii. Example

If you would like to see an example of the calculator's working, just click the "example" button.

#### iii. Solutions

As mentioned earlier, the calculator won't just tell you the answer but also the steps you can follow to do the calculation yourself. The "show/hide solution" button would be available to you after the calculator has processed your input.

#### iv. Share

We would love to see you share our calculators with your family, friends, or anyone else who might find it useful.

By checking the "include calculation" checkbox, you can share your calculation as well.

Here's a quick overview of what "mean" is and how to calculate it.

## Mean

Mean is a measure of the central tendency of a group of values. It is an estimate of a typical value in that group.

Mean is defined as the ratio of the sum of values in the group and the number of values.

So, for a group of $\hspace{0.2em} n \hspace{0.2em}$ numbers $\hspace{0.2em} x_1 \hspace{0.2em}$, $\hspace{0.2em} x_2 \hspace{0.2em}$, $\hspace{0.2em} x_3 \hspace{0.2em}$, ... $\hspace{0.2em} x_n \hspace{0.2em}$, the mean $\hspace{0.2em} \overline{x} \hspace{0.2em}$ would be

$\overline{x} \hspace{0.25em} = \hspace{0.25em} \frac{x_1 + x_2 + x_3 + ... + x_n}{n}$

A shorthand version of the same formula is

$\overline{x} \hspace{0.25em} = \hspace{0.25em} \frac{\Sigma \hspace{0.2em} x_n}{n}$

Example

The ages of five participants in a coding bootcamp are $\hspace{0.2em} 25 \hspace{0.2em}$, $\hspace{0.2em} 29 \hspace{0.2em}$, $\hspace{0.2em} 30 \hspace{0.2em}$, $\hspace{0.2em} 32 \hspace{0.2em}$, and $\hspace{0.2em} 36 \hspace{0.2em}$ years old. Calculate their mean age.

Solution

Based on what we learned earlier, to get the mean age $\hspace{0.2em} \overline{x} \hspace{0.2em}$, we divide the sum of their ages by the number of the participants.

$\begin{align*} \overline{x} \hspace{0.25em} &= \hspace{0.25em} \frac{25 + 29 + 30 + 32 + 36}{5} \\[1.5em] &= \hspace{0.25em} 30.4 \end{align*}$

So the mean age is $\hspace{0.2em} 30.4 \hspace{0.2em}$ years.

### Weighted Mean

There are cases where, in a dataset, the different observations or values do not share the same importance. Some are more important than others. In such cases, simple mean may not be very useful. Instead, the weighted mean is more prefereable.

So here's what we do.

We assign each value $\hspace{0.2em} x_r \hspace{0.2em}$ a weight of $\hspace{0.2em} w_r \hspace{0.2em}$. And then we can calculate the weighted mean using the formula

$\overline{x} \hspace{0.2em} = \hspace{0.2em} \frac{x_1 w_1 + x_2 w_2 + x_3 w_3 + ... + x_n w_n}{w_1 + w_2 + w_3 + ... + w_n}$

Now, this formula can be rewritten as

$\overline{x} \hspace{0.2em} = \hspace{0.2em} \frac{\Sigma \hspace{0.2em} x_n w_n}{\Sigma \hspace{0.2em} w_n}$

Example

A car sales agency is analyzing its quarterly sales data. They sold 100, 120, and 140 cars in the first, second, and third quarters respectively. However, in the fourth quarter, they had a significant increase, with 300 cars sold. Calculate the weighted mean of the quarterly sales data, considering the weights of each quarter as 2, 2, 3, and 4, respectively.

Solution

Using the formula for weighted mean, we have —

$\begin{align*} \overline{x} \hspace{0.25em} &= \hspace{0.25em} \frac{2 \times 100 + 2 \times 120 + 3 \times 140 + 4 \times 300 }{2 + 2 + 3 + 4} \\[1.75em] &= \hspace{0.25em} \frac{2060}{11} \\[1.75em] &= \hspace{0.25em} 187.27 \end{align*}$

And that's it.