Mean, Median, Mode Calculator

How to Calculate Mean, Median, and Mode

Mean, median, and mode are three key measures of central tendency in statistics. They help us understand the typical or central value in a dataset.

Mean Formula

The mean is the average of all numbers in a dataset. The formula for calculating the mean is:

\[ \text{Mean} = \frac{\sum_{i=1}^{n} x_i}{n} \]

Where:

• \(x_i\) represents each value in the dataset
• \(n\) is the number of values in the dataset

Median Definition

The median is the middle value when a dataset is ordered from least to greatest. For an odd number of values, it's the middle number. For an even number of values, it's the average of the two middle numbers.

Mode Definition

The mode is the value that appears most frequently in a dataset. A dataset can have one mode, more than one mode (multimodal), or no mode.

Calculation Steps

1. Sort the dataset in ascending order
2. Calculate the mean by summing all values and dividing by the count
3. Find the median by identifying the middle value(s)
4. Determine the mode by finding the most frequent value(s)
5. Calculate additional measures like sum, count, min, max, and range

Example

Let's calculate the mean, median, and mode for the dataset: 4, 7, 9, 3, 2, 7

1. Sort the dataset: 2, 3, 4, 7, 7, 9
2. Calculate the mean:

   \[ \text{Mean} = \frac{2 + 3 + 4 + 7 + 7 + 9}{6} = \frac{32}{6} = 5.33 \]

3. Find the median:

   With 6 values, we average the two middle numbers: (4 + 7) / 2 = 5.5

4. Determine the mode: 7 (appears twice)
5. Additional calculations:
   • Sum: 32
   • Count: 6
   • Minimum: 2
   • Maximum: 9
   • Range: 9 - 2 = 7

Visual Representation

This diagram illustrates the mean, median, and mode for the example dataset. The green line represents the mean, the red dashed line shows the median, and the yellow circle indicates the mode. Blue dots represent individual data points.