Statistics Calculator

About the Statistics Calculator

Calculates the key descriptive statistics for a dataset: count, sum, mean, median, mode, range, population variance and standard deviation.

How to use this calculator

1. Enter your data values, usually separated by commas or spaces.
2. Choose whether you want mean, median, mode, variance, or standard deviation.
3. Click calculate to see the results instantly.
4. Use the step-by-step output to check how each value was found.

The formula explained

The formula \( \sigma = \sqrt{\frac{\sum (x_i-\bar{x})^2}{n}} \) computes the population standard deviation, which measures the typical distance of the data values from the mean. A larger standard deviation means the data are more spread out.

• \(x_i\) = the i-th data value
• \(\bar{x}\) = the mean, or average, of the data set
• n = the number of values in the data set
• \(\sigma\) = the population standard deviation

Step by step method

1. Find the mean by adding all values and dividing by the number of values.
2. Subtract the mean from each value, square each difference, and add the squared differences.
3. Divide by n for population variance, then take the square root to get standard deviation.

Worked example

Problem. Find the mean, median, mode, variance, and standard deviation of the data set 2, 4, 4, 6, 8.

1. Mean: \( (2+4+4+6+8)/5 = 24/5 = 4.8 \). Median: the middle value is 4.
2. Mode: 4 appears twice, more than any other value.
3. Population variance: \( [(2-4.8)^2+(4-4.8)^2+(4-4.8)^2+(6-4.8)^2+(8-4.8)^2]/5 = (7.84+0.64+0.64+1.44+10.24)/5 = 20.8/5 = 4.16 \). Standard deviation: \( \sqrt{4.16} \approx 2.04 \).

Tips and common mistakes

• Check whether you need population variance and standard deviation, which divide by n, or sample versions, which divide by n-1.
• If your data have no repeated values, there may be no mode.

Frequently asked questions