Sample Mean Calculator

Calculate the arithmetic mean (average) of a dataset. Get the sum, count, and step-by-step calculation.

Data Input Method

Decimal Places

Data Set

Enter numbers separated by commas, spaces, or new lines

Value (x)

Frequency (f)

Enter each unique value and how many times it occurs

Lower Bound

Upper Bound

Frequency (f)

For grouped data, enter class intervals and frequencies. Midpoints will be calculated automatically.

Sample Mean (x̄)

Sum & Count

Data Summary

Step-by-Step Solution

Enter data and click "Calculate" to see the step-by-step solution.

Sample Mean Formula

x̄ = Σxᵢ / n

Where:

x̄ = sample mean
Σxᵢ = sum of all values
n = number of observations

Understanding the Mean

The mean is the average of all data points
It represents the central tendency of the data
Can be affected by outliers (extreme values)
Also called the arithmetic mean

When to Use

Finding average test scores
Calculating average income
Quality control analysis
Research data analysis
Business performance metrics

Frequently Asked Questions

What is the sample mean?

The sample mean (represented by x̄) is the average of a set of numbers. It's calculated by adding all values together and dividing by the number of values. It represents the central tendency of the data.

How do you calculate the sample mean?

Step 1: Add all the numbers in your dataset (find the sum)

Step 2: Count how many numbers you have (find n)

Step 3: Divide the sum by the count: x̄ = Σx / n

What's the difference between sample mean and population mean?

Sample mean (x̄) is calculated from a subset of data, while population mean (μ) uses all data points. Both use the same formula, but sample mean is an estimate when you can't measure the entire population.

Can the mean be negative?

Yes, the mean can be negative if most or all of your data points are negative values. For example, the mean of -5, -3, -2, -4 is -3.5.

What is the mean of 10, 20, and 30?

Sum: 10 + 20 + 30 = 60

Count: 3 numbers

Mean: 60 ÷ 3 = 20