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Descriptive statisticsStatistics and probabilityHigh schoolabout 0:50

Find the population standard deviation of 50, 55, 60, 65, 70, 75, 80: animated lesson

A narrated, step-by-step descriptive statistics video lesson with captions. Final answer: σ = 10.

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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 (0.3 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Standard deviation
Find the population standard deviation of 50, 55, 60, 65, 70, 75, 80.
2. Steps, part 1
1. $\bar{x} = \frac{455}{7} = 65$
  Find the mean
2. $(50 - 65)^2 = 225 \\ (55 - 65)^2 = 100 \\ (60 - 65)^2 = 25 \\ (65 - 65)^2 = 0 \\ (70 - 65)^2 = 25 \\ (75 - 65)^2 = 100 \\ (80 - 65)^2 = 225$
  Square each deviation from the mean
3. $\sum (x_i - \bar{x})^2 = 700$
  Add the squared deviations
4. $\sigma^2 = \frac{700}{7} = 100$
  Divide by n to get the population variance
3. Steps, part 2
1. $\sigma = \sqrt{100} = 10$
  Take the square root
4. The answer
$\sigma = 10$
σ = √(700/7) = 10
5. Check
- Variance = 100, and 10² = 100
- Sample SD for comparison: 10.8012345

Transcript

The problem. Here is the problem: Find the population standard deviation of 50, 55, 60, 65, 70, 75, 80. Treat the data as the entire population (divide by n).

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

Steps, part 2. Take the square root.

The answer. So the answer is σ equals 10. 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 100, and 10 squared equals 100. Sample SD for comparison: 10.8012345.

About descriptive statistics

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

Find the population standard deviation of 50, 55, 60, 65…