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Descriptive statisticsStatistics and probabilityMiddle schoolabout 1:04

Standard deviation of 2, 4, 4, 4, 5, 5, 7, 9: animated lesson

A narrated, step-by-step descriptive statistics video lesson with captions. Final answer: s = 2.138089935.

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. 1. The problem
    Standard deviation
    Sample standard deviation of 2, 4, 4, 4, 5, 5, 7, 9
  2. 2. Steps, part 1
    1. xˉ=408=5\bar{x} = \frac{40}{8} = 5
      Find the mean
    2. (2−5)2=9(4−5)2=1(4−5)2=1(4−5)2=1(5−5)2=0(5−5)2=0(7−5)2=4(9−5)2=16(2 - 5)^2 = 9 \\ (4 - 5)^2 = 1 \\ (4 - 5)^2 = 1 \\ (4 - 5)^2 = 1 \\ (5 - 5)^2 = 0 \\ (5 - 5)^2 = 0 \\ (7 - 5)^2 = 4 \\ (9 - 5)^2 = 16
      Square each deviation from the mean
    3. ∑(xi−xˉ)2=32\sum (x_i - \bar{x})^2 = 32
      Add the squared deviations
    4. s2=327=4.571428571s^2 = \frac{32}{7} = 4.571428571
      Divide by n − 1 to get the sample variance
  3. 3. Steps, part 2
    1. s=4.571428571=2.138089935s = \sqrt{4.571428571} = 2.138089935
      Take the square root
  4. 4. The answer
    s=2.138089935s = 2.138089935

    s = √(32 / 7) = 2.138089935

  5. 5. Check
    • Variance = 4.571428571, and 2.138089935² = 4.571428571
    • Population SD for comparison: 2

Transcript

The problem. Here is the problem: Sample standard deviation of 2, 4, 4, 4, 5, 5, 7, 9. 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 2.138089935. 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 4.571428571, and 2.138089935 squared equals 4.571428571. Population SD for comparison: 2.

About descriptive statistics

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

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Standard deviation of 2, 4, 4, 4, 5, 5, 7, 9 (Lesson)