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Descriptive statisticsStatistics and probabilityMiddle schoolabout 0:59

Variance of 1, 2, 3, 4, 5: animated lesson

A narrated, step-by-step descriptive statistics video lesson with captions. Final answer: s² = 2.5.

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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
Worked example
Sample standard deviation of 1, 2, 3, 4, 5
2. Steps, part 1
1. $\bar{x} = \frac{15}{5} = 3$
  Find the mean
2. $(1 - 3)^2 = 4 \\ (2 - 3)^2 = 1 \\ (3 - 3)^2 = 0 \\ (4 - 3)^2 = 1 \\ (5 - 3)^2 = 4$
  Square each deviation from the mean
3. $\sum (x_i - \bar{x})^2 = 10$
  Add the squared deviations
4. $s^2 = \frac{10}{4} = 2.5$
  Divide by n − 1 to get the sample variance
3. Steps, part 2
1. $s = \sqrt{2.5} = 1.58113883$
  Take the square root
4. The answer
$s^2 = 2.5$
s² = 2.5
5. Check
- Variance = 2.5, and 1.58113883² = 2.5
- Population SD for comparison: 1.414213562

Transcript

The problem. Here is the problem: Sample standard deviation of 1, 2, 3, 4, 5. Treat the data as a sample from a larger population (Bessel prime s correction, divide by n minus 1). The variance is the square of the standard deviation.

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 squared equals 2.5. 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 2.5, and 1.58113883 squared equals 2.5. Population SD for comparison: 1.414213562.

About descriptive statistics

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

Variance of 1, 2, 3, 4, 5: Animated Step-by-Step Lesson