Mode, Median, and Mean Calculator

What are Mode, Median, and Mean?

Mode, median, and mean are three different measures of central tendency in statistics. They help us understand the typical or central value in a dataset.

Formulas and Their Meanings

1. Mean (\(\bar{x}\)): \[\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}\] Where \(x_i\) are individual values and \(n\) is the number of values. The mean is the average of all values.

2. Median: \[ \text{Median} = \begin{cases} x_{(\frac{n+1}{2})}, & \text{if n is odd} \\ \frac{x_{(\frac{n}{2})} + x_{(\frac{n}{2}+1)}}{2}, & \text{if n is even} \end{cases} \] The median is the middle value when the data is ordered.

3. Mode: The mode is the value that appears most frequently in the dataset. There is no specific formula, as it's determined by counting occurrences.

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.

Example Calculation

Let's calculate for the dataset: 2, 3, 4, 4, 5, 5, 5, 6, 7

1. Mean: \(\bar{x} = \frac{2 + 3 + 4 + 4 + 5 + 5 + 5 + 6 + 7}{9} = \frac{41}{9} \approx 4.56\)
2. Median: The middle value is 5
3. Mode: 5 (appears three times, more than any other value)

Visual Representation

This scatter plot represents the example dataset. The red dashed line indicates the mean (4.56), the green dashed line shows the median (5), and the blue dashed line represents the mode (5). Note that in this case, the median and mode coincide.