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Descriptive statisticsStatistics and probabilityHigh schoolabout 1:00

Find the sample standard deviation of 4, 8, 6, 5, 3, 7: animated lesson

A narrated, step-by-step descriptive statistics video lesson with captions. Final answer: s = 1.870828693.

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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
Standard deviation
Find the sample standard deviation of 4, 8, 6, 5, 3, 7.
2. Steps, part 1
1. $\bar{x} = \frac{33}{6} = 5.5$
  Find the mean
2. $(4 - 5.5)^2 = 2.25 \\ (8 - 5.5)^2 = 6.25 \\ (6 - 5.5)^2 = 0.25 \\ (5 - 5.5)^2 = 0.25 \\ (3 - 5.5)^2 = 6.25 \\ (7 - 5.5)^2 = 2.25$
  Square each deviation from the mean
3. $\sum (x_i - \bar{x})^2 = 17.5$
  Add the squared deviations
4. $s^2 = \frac{17.5}{5} = 3.5$
  Divide by n − 1 to get the sample variance
3. Steps, part 2
1. $s = \sqrt{3.5} = 1.870828693$
  Take the square root
4. The answer
$s = 1.870828693$
s = √(17.5 / 5) = 1.870828693
5. Check
- Variance = 3.5, and 1.870828693² = 3.5
- Population SD for comparison: 1.707825128

Transcript

The problem. Here is the problem: Find the sample standard deviation of 4, 8, 6, 5, 3, 7. 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 1.870828693. 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 3.5, and 1.870828693 squared equals 3.5. Population SD for comparison: 1.707825128.

About descriptive statistics

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

Find the sample standard deviation of 4, 8, 6, 5, 3, 7