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Descriptive statisticsStatistics and probabilityHigh schoolabout 1:10

Find the sample standard deviation of 10, 12, 23, 23, 16, 23, 21, 16: animated lesson

A narrated, step-by-step descriptive statistics video lesson with captions. Final answer: s = 5.237229366.

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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 (0.5 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Standard deviation
Find the sample standard deviation of 10, 12, 23, 23, 16, 23, 21, 16.
2. Steps, part 1
1. $\bar{x} = \frac{144}{8} = 18$
  Find the mean
2. $(10 - 18)^2 = 64 \\ (12 - 18)^2 = 36 \\ (23 - 18)^2 = 25 \\ (23 - 18)^2 = 25 \\ (16 - 18)^2 = 4 \\ (23 - 18)^2 = 25 \\ (21 - 18)^2 = 9 \\ (16 - 18)^2 = 4$
  Square each deviation from the mean
3. $\sum (x_i - \bar{x})^2 = 192$
  Add the squared deviations
4. $s^2 = \frac{192}{7} = 27.42857143$
  Divide by n − 1 to get the sample variance
3. Steps, part 2
1. $s = \sqrt{27.42857143} = 5.237229366$
  Take the square root
4. The answer
$s = 5.237229366$
s = √(192/7) = 5.237229366
5. Check
- Variance = 27.42857143, and 5.237229366² = 27.42857143
- Population SD for comparison: 4.898979486

Transcript

The problem. Here is the problem: Find the sample standard deviation of 10, 12, 23, 23, 16, 23, 21, 16. 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 5.237229366. 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 27.42857143, and 5.237229366 squared equals 27.42857143. Population SD for comparison: 4.898979486.

About descriptive statistics

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

Find the sample standard deviation of 10, 12, 23, 23, 16…