Mean, Median, Mode, Range, Midrange Calculator

Understanding Statistical Measures: Mean, Median, Mode, Range, and Midrange

What are these measures?

These are fundamental statistical measures used to describe and summarize a set of data:

• Mean: The average of all numbers in a dataset.
• Median: The middle value when the dataset is ordered.
• Mode: The most frequently occurring value(s) in the dataset.
• Range: The difference between the largest and smallest values in the dataset.
• Midrange: The average of the maximum and minimum values in the dataset.

Formulas and Their Components

Mean: \(\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}\)

Where \(\bar{x}\) is the mean, \(\sum\) means "sum of", \(x_i\) are individual values, and \(n\) is the total number of values.

Median: The middle value when the dataset is ordered (or average of two middle values if \(n\) is even).

Mode: No formula; it's the most frequent value(s) in the dataset.

Range: \(R = x_{max} - x_{min}\)

Where \(R\) is the range, \(x_{max}\) is the largest value, and \(x_{min}\) is the smallest value.

Midrange: \(MR = \frac{x_{max} + x_{min}}{2}\)

Where \(MR\) is the midrange, \(x_{max}\) is the largest value, and \(x_{min}\) is the smallest value.

Calculation Steps

1. Sort the dataset in ascending order.
2. For Mean: Sum all numbers and divide by the count.
3. For Median: Find the middle value(s).
4. For Mode: Identify the most frequent value(s).
5. For Range: Subtract the smallest from the largest value.
6. For Midrange: Add the smallest and largest values, then divide by 2.

Example Calculation

Let's calculate these measures for the dataset: 2, 4, 4, 6, 8, 10

1. Mean: \(\frac{2 + 4 + 4 + 6 + 8 + 10}{6} = \frac{34}{6} = 5.67\)
2. Median: With 6 numbers, we average the 3rd and 4th: \(\frac{4 + 6}{2} = 5\)
3. Mode: 4 (appears twice)
4. Range: \(10 - 2 = 8\)
5. Midrange: \(\frac{10 + 2}{2} = 6\)

Visual Representation

This bar chart visualizes our example dataset. Each blue bar represents a data point. The colored dashed lines indicate different statistical measures:

• Red dashed line: Mean (5.67)
• Green dashed line: Median (5)
• Blue dashed line: Mode (4)
• Orange dashed line: Range (8)
• Purple dashed line: Midrange (6)

This visual representation helps to understand the relationship between these different statistical measures and the distribution of the data points.