Mean, Median, Mode, Range Calculator | Best Calculator

Mean, Median, Mode & Range Calculator

Result
Mean (Average): 5.333
Median: 5
Range: 8
Mode: 5 (appeared 3 times)
Largest: 10
Smallest: 2
Sum: 48
Count: 9
Sorted Data Set: 2, 3, 3, 5, 5, 5, 7, 8, 10
Column Chart of the Values
Formulas:
Mean = Sum of all numbers ÷ Count of numbers
Median = Middle value (or average of two middle values)
Mode = Most frequently occurring number(s)
Range = Highest value - Lowest value
Example:Data Set:
Data Set: 5, 3, 8, 7, 5, 10, 2, 5, 3
Sorted Data Set: 2, 3, 3, 5, 5, 5, 7, 8, 10
Mean: (2 + 3 + 3 + 5 + 5 + 5 + 7 + 8 + 10) / 9 = 5.33
Median: 5 (middle value in sorted list)
Mode: 5 (appeared 3 times) &nbsp Range: 10 - 2 = 8
Largest: 10 &nbspSmallest: 2 &nbspSum: 48 &nbspCount: 9
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Mean (Average)

In statistics and mathematics, the term “mean” most commonly refers to the arithmetic mean, also known as the average. While “mean” can have different meanings in various contexts, in basic data analysis, it represents the central value of a group of numbers.

To calculate the mean, simply add all the numbers in a data set and divide the total by the number of values:

Formula:
Mean = (Sum of all values) / (Total number of values)

For example, in the data set:
10, 2, 38, 23, 38, 23, 21

Mean = (10 + 2 + 38 + 23 + 38 + 23 + 21) ÷ 7 = 22.14

In notation, the mean is often shown as x̄ (x-bar), while the population mean uses the Greek letter μ (mu).

There are also other types of means, like the weighted mean and the geometric mean, but the arithmetic mean is the most commonly used.

Median

The median is the middle value of a data set when all values are arranged in order. It’s a useful measure of central tendency, especially when the data contains outliers or extreme values.

To find the median:

  1. Sort the data in ascending or descending order.

  2. If the total number of values is odd, the median is the middle number.

  3. If the number of values is even, the median is the average of the two middle numbers.

Example:
Data set: 2, 10, 21, 23, 23, 38, 38
Since there are 7 values (odd), the median is 23.

Now, if we add an outlier:
Data set: 2, 10, 21, 23, 23, 38, 38, 1027892
Now there are 8 values (even), and the two middle values are both 23. So, the median remains 23.

Even with a large outlier, the median stays stable, which is why it’s often a better measure than the mean in skewed data.

Mode

The mode is the value that appears most frequently in a data set. A data set can have one mode, more than one mode, or no mode at all if no number repeats.

Example:
Data set: 2, 10, 21, 23, 23, 38, 38
Here, both 23 and 38 appear twice, so the data set is bimodal.

Unlike the mean and median, the mode can also be used for non-numerical data. For example, if a store sells more XOCHiTL tortilla chips than any other brand, XOCHiTL is the mode of chip sales. This can help businesses make better stocking decisions.

Range

The range shows how spread out the numbers in a data set are. It is calculated by subtracting the smallest value from the largest value.

Formula:
Range = Highest value – Lowest value

Example:
Data set: 2, 10, 21, 23, 23, 38, 38
Range = 38 – 2 = 36

Now, if we include an outlier:
Data set: 2, 10, 21, 23, 23, 38, 38, 1027892
Range = 1027892 – 2 = 1,027,890

As shown, extreme values can significantly affect the range, so it’s best used alongside other statistics like the mean and median to get a complete picture of the data.

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