Solve a problem

Descriptive statisticsStatistics and probabilityMiddle schoolabout 1:02

Standard deviation of 1, 2, 3, 4: animated lesson

A narrated, step-by-step descriptive statistics video lesson with captions. Final answer: s = 1.290994449.

SpeedLanguage

Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.4 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Standard deviation
Sample standard deviation of 1, 2, 3, 4
2. Steps, part 1
1. $\bar{x} = \frac{10}{4} = 2.5$
  Find the mean
2. $(1 - 2.5)^2 = 2.25 \\ (2 - 2.5)^2 = 0.25 \\ (3 - 2.5)^2 = 0.25 \\ (4 - 2.5)^2 = 2.25$
  Square each deviation from the mean
3. $\sum (x_i - \bar{x})^2 = 5$
  Add the squared deviations
4. $s^2 = \frac{5}{3} = 1.666666667$
  Divide by n − 1 to get the sample variance
3. Steps, part 2
1. $s = \sqrt{1.666666667} = 1.290994449$
  Take the square root
4. The answer
$s = 1.290994449$
s = √(5 / 3) = 1.290994449
5. Check
- Variance = 1.666666667, and 1.290994449² = 1.666666667
- Population SD for comparison: 1.118033989

Transcript

The problem. Here is the problem: Sample standard deviation of 1, 2, 3, 4. Treat the data as a sample from a larger population (Bessel prime s correction, divide by n minus 1).

Steps, part 1. Find the mean. Square each deviation from the mean. Add the squared deviations. Divide by n minus 1 to get the sample variance.

Steps, part 2. Take the square root.

The answer. So the answer is s equals 1.290994449. Standard deviation measures how spread out the values are around the mean. A small value means the data are clustered near the mean.

Check. Variance equals 1.666666667, and 1.290994449 squared equals 1.666666667. Population SD for comparison: 1.118033989.

About descriptive statistics

Mean, median, mode, range, variance and standard deviation of a data set.

Standard deviation of 1, 2, 3, 4: Step-by-Step Lesson