# Mean Median Mode Calculator

The tool doesn't count empty cells or non-numeric cells.

### What is the difference between mean, median, and mode?

The mean, median, and mode are measures of central tendency.

The mean is the arithmetic average, the median is the middle value of a sorted set of numbers, and the mode is the value that appears most often. If the distribution is perfectly symmetrical, the **mean** and **median** will have the same value.

When the distribution is perfectly symmetrical and has only one mode, the **mean**, **median**, and **mode** will have the same value.

### What is the mean?

The mean is a value that represents the middle of a set of numbers.

Usually, the *mean* refers to the *arithmetic mean* or *arithmetic average*.

### How do you calculate the mean?

1. Add up all the numbers.

2. Count how many numbers there are.

3. Divide the sum by the count.

### Mean formula

x̄ = | Σ𝑥_{i} |

n |

**n**- sample size, the total number of values.

**Σx**- the addition of all the values.

_{i}### What is the median?

When you sort a list of values, the median is the middle value. For an odd number of values, there is exactly one value in the middle, which is the median. For an even number of values, there are two numbers in the middle, and the median is the average of these two numbers.

### How to calculate the median?

1. Sort the numbers in ascending order.

2. Count how many numbers there are, **n**.

3. If n is an **odd** number, the median is the middle number, specifically the (n+1)/2^{th} number.

4. If n is an **even** number, the median is the average of the two middle numbers, specifically the (n/2)^{th} number, and the (n/2+1)^{th} number.

### Median formula

__1. Odd number of values (n)__:**Median = x _{(n+1)/2}**

__2. Even number of values (n)__:

Median = | X_{n/2} + X_{(n/2+1)} |

2 |

### What is the difference between sample mean and population mean?

The population mean (μ) is the mean of the entire population.

Sample mean (x̄) is the mean of a random sample of data.

Usually, we don't have data for the entire population, so we use the sample mean to estimate the population mean.

### How to calculate the mode

1. Sort the numbers in ascending order.

2. Count how many times each number appears.

3. Check which number or numbers appear most frequently; this number is the mode.

If no value appears more than once, for example for with a continuous variable, you can create a histogram and identify the bin with the highest count; the mode is the midpoint of this bin.

### Mode formula

Count(x_{j})=Max_{i}(Count(x_{i}))

**Group Data mode**

Mode = L + h | f_{x} - f_{1} |

2f_{x} - f_{1} - f_{2} |

Choose bin **x** with the highest frequency.

f_{x} - the frequency of bin x.

L - lower limit of bin x.

f_{1} - the frequency of the bin to the left (lower bin).

f_{2} - the frequency of the bin to the right (upper bin).

h - bin size.

Example

Name | Bin | Frequency |
---|---|---|

0 - 10 | 5 | |

1 | 10 - 20 | 18 |

x | 20 - 30 | 23 |

2 | 30 - 40 | 15 |

40 - 50 | 13 |

Mode = 20 + 10 * | 23 - 18 | = 23.846 |

2*23 - 18 - 15 |

### Should I use average or median?

Both average and median measure the central tendency of the data. Usually, we use the average statistic.

We prefer the median in the following cases:

1. The data contains outliers.

2. The data is very skewed, and the sample size is not large

In these cases, one outlier or one rare extreme value might change the average dramatically.

The median is not affected by extreme values.

### Outliers

It is **not** recommended to exclude the outliers unless you know the reason for each outlier.

We use the Tukey's Fences method with k = 1.5.

For more options, you may use the Outliers calculator

### Round

When the number is greater than 1, it will round to decimal places, for smaller number it will round to precision.

Example, digits = 2, format 0.001234 to 0.0012, and 88.1234 to 88.12