Question 1

What is standard deviation?

Accepted Answer

Standard deviation measures how spread out data points are from the mean. A low standard deviation means data points cluster closely around the mean, while a high standard deviation indicates wider spread. It's the square root of variance and is widely used in statistics, finance, and science.

Question 2

What is the difference between population and sample standard deviation?

Accepted Answer

Population standard deviation (σ) divides by N — used when your data represents an entire population. Sample standard deviation (s) divides by N-1 (Bessel's correction) — used when your data is a sample from a larger population. The sample version gives an unbiased estimate of the population parameter.

Question 3

How do I calculate standard deviation by hand?

Accepted Answer

1) Find the mean of your data. 2) Subtract the mean from each data point and square the result. 3) Sum all squared differences. 4) Divide by N (population) or N-1 (sample). 5) Take the square root. For example, data [2,4,4,4,5,5,7,9] has mean 5, variance 4, and standard deviation 2.

Question 4

What is a good standard deviation?

Accepted Answer

There's no universal 'good' value — it depends on context. In test scores, a lower SD means consistent results. In investments, a higher SD means more volatility/risk. Coefficient of variation (SD/mean × 100%) is often more useful for comparing spread across different datasets.

Question 5

What is variance?

Accepted Answer

Variance is the average of squared differences from the mean. Standard deviation is its square root. Variance is measured in squared units, making it harder to interpret directly. For example, if data is in meters, variance is in square meters, while standard deviation remains in meters.

Question 6

What are quartiles?

Accepted Answer

Quartiles divide sorted data into four equal parts. Q1 (25th percentile) is the median of the lower half, Q2 (50th) is the overall median, and Q3 (75th percentile) is the median of the upper half. The interquartile range (IQR = Q3 - Q1) shows the middle 50% spread and is robust against outliers.

Question 7

What is the empirical rule (68-95-99.7)?

Accepted Answer

For normally distributed data, approximately 68% of data falls within 1 standard deviation of the mean, 95% within 2 SDs, and 99.7% within 3 SDs. This rule helps quickly assess how typical or unusual a data point is in a normal distribution.

Question 8

How do outliers affect standard deviation?

Accepted Answer

Standard deviation is sensitive to outliers because it uses squared differences. A single extreme value can significantly inflate the SD. For skewed data or datasets with outliers, consider using the median and IQR instead, which are more robust measures of central tendency and spread.

Standard Deviation Calculator

Enter Your Data

Descriptive Statistics

Histogram

Box Plot

How to Use This Standard Deviation Calculator