Median Calculator

 

Mean, Median, Mode Calculator: Understanding Central Tendency

Calculate mean, median, mode along with the minimum, maximum, range, count, and sum for a set of data. Enter values separated by commas or spaces. You can also copy and paste lines of data from spreadsheets or text documents. See all allowable formats in the table below.

What are Mean, Median, and Mode?

Mean, median, and mode are measures of central tendency in statistics, providing insights into what values in a dataset are typical or representative. Each has a unique way of characterizing the data:

Mean (Average)

The mean is the average value of a dataset, calculated by adding up all the numbers and dividing by the count of numbers in the dataset.

Mean Formula

\[ \bar{x} = \frac{\sum_{i=1}^{n}x_i}{n} \]

Median

The median is the central number of a dataset. Arrange data points from smallest to largest and locate the central number. If there are two numbers in the middle, the median is the average of those two numbers.

Median Formula

If \( n \) is odd, the median is the value at position \( p \) where \( p = \frac{n + 1}{2} \). If \( n \) is even, the median is the average of the values at positions \( p \) and \( p + 1 \) where \( p = \frac{n}{2} \).

Mode

The mode is the number in a dataset that occurs most frequently. If there is more than one mode, or all numbers occur the same number of times, there is no mode.

Additional Measures: Interquartile Range and Outliers

The Interquartile Range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). Outliers are values that lie above the Upper Fence or below the Lower Fence of the sample set.

\[ IQR = Q3 - Q1 \]

Potential Outliers are determined by the Upper Fence (\( Q3 + 1.5 \times IQR \)) and Lower Fence (\( Q1 - 1.5 \times IQR \)).

Frequently Asked Questions

• How do I calculate the median?
  Calculate the median by arranging data values and finding the middle value or the average of two middle values.
• What is the median of 3, 7, 2, 4, 7, 5, 7, 1, 8, 8?
  Arrange the data, and find the middle value or average of the two middle values.
• What is the median of 3, 6, 9, 7, 4, 6, 7, 0, 7?
  Follow the same process to find the median by arranging data values.
• What is the median of 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10?
  Arrange the data and find the middle value or average of two middle values.
• How do I calculate the median?
  Calculate the median by arranging data values and finding the middle value or the average of two middle values.
• What is the median of 3, 7, 2, 4, 7, 5, 7, 1, 8, 8?
  Arrange the data, and find the middle value or average of the two middle values.
• What is the median of 3, 6, 9, 7, 4, 6, 7, 0, 7?
  Follow the same process to find the median by arranging data values.
• What is the median of 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10?
  Arrange the data and find the middle value or average of two middle values.
• What is the median of 2, 9, 3, 7, 5, 4, 3, 2, 10?
  Organize the data and determine the middle value or average of the two middle values.
• What is the median of 1, 2, 3, 4, 10?
  Arrange the values and find the middle value or average of the two middle values (since there are two).
• What is the median of 7, 3, 5, 8, 6, 10, 9, and 12?
  Arrange the numbers and determine the middle value or average of two middle values.
• What is the median of 7, 6, 4, 8, 2, 5, and 11?
  Organize the data and find the middle value or average of two middle values (if even).
• What is the median of 5, 7, 9, 11, 15, 17, 2, 23, and 19?
  Arrange the numbers and determine the middle value or average of two middle values.
• What is the mean deviation of 3, 10, 10, 4, 7, 10, 5?
  Calculate the mean deviation by finding the average of the absolute differences between each value and the mean of the set.
• What is the mean and standard deviation of 1, 2, 3, 4, 5, 6?
  Calculate both the mean and standard deviation using their respective formulas.