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Descriptive statisticsStatistics and probabilityHigh schoolabout 1:02

Find the sample standard deviation of 15, 18, 21, 24, 27, 30: animated lesson

A narrated, step-by-step descriptive statistics video lesson with captions. Final answer: s = 5.61248608.

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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 15, 18, 21, 24, 27, 30.
2. Steps, part 1
1. $\bar{x} = \frac{135}{6} = 22.5$
  Find the mean
2. $(15 - 22.5)^2 = 56.25 \\ (18 - 22.5)^2 = 20.25 \\ (21 - 22.5)^2 = 2.25 \\ (24 - 22.5)^2 = 2.25 \\ (27 - 22.5)^2 = 20.25 \\ (30 - 22.5)^2 = 56.25$
  Square each deviation from the mean
3. $\sum (x_i - \bar{x})^2 = 157.5$
  Add the squared deviations
4. $s^2 = \frac{157.5}{5} = 31.5$
  Divide by n − 1 to get the sample variance
3. Steps, part 2
1. $s = \sqrt{31.5} = 5.61248608$
  Take the square root
4. The answer
$s = 5.61248608$
s = √(157.5 / 5) = 5.61248608
5. Check
- Variance = 31.5, and 5.61248608² = 31.5
- Population SD for comparison: 5.123475383

Transcript

The problem. Here is the problem: Find the sample standard deviation of 15, 18, 21, 24, 27, 30. 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 5.61248608. 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 31.5, and 5.61248608 squared equals 31.5. Population SD for comparison: 5.123475383.

About descriptive statistics

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

Find the sample standard deviation of 15, 18, 21, 24, 27, 30