"What is the standard deviation of the following..." was answered by our community

trefoniu1

Answered question

2022-01-29

What is the standard deviation of the following numbers: 24, 36, 33, 21, 15, 11?

Answer & Explanation

mihady54

Beginner2022-01-30Added 13 answers

Explanation:
We know:

σ^{2} = \frac{\sum x^{2}}{n} - {(\frac{\sum x}{n})}^{2}

\sum x = 24 + 36 + 33 + 21 + 15 + 11 = 140

\sum x^{2} = 24^{2} + 36^{2} + 33^{2} + 21^{2} + 15^{2} + 11^{2} = 3748

n is the number data in the sample,

\Rightarrow n = 6

Hence plugging into the formula:

σ^{2} = \frac{3748}{6} - {(\frac{140}{6})}^{2} = \frac{722}{9}

\Rightarrow σ = \frac{\sqrt{722}}{\sqrt{9}} = \frac{19 \sqrt{2}}{3}

Devyn Figueroa

Beginner2022-01-31Added 10 answers

Explanation:
Mean for the given numbers

= \frac{24 + 36 + 33 + 21 + 15 + 11}{6} = 23.33

Variance

σ^{2} = \sum \frac{{(x - \overset{―}{x})}^{2}}{n}

σ^{2} = \sum \frac{{(23.33 - 24)}^{2} + {(23.33 - 36)}^{2} + {(23.33 - 33)}^{2} + {(23.33 - 21)}^{2} + {(23.33 - 15)}^{2} + {(23.33 - 11)}^{2}}{6}

σ^{2} = \frac{{(- 0.67)}^{2} + {(- 12.67)}^{2} + {(- 9.67)}^{2} + {(2.33)}^{2} + {(8.33)}^{2} + {(12.33)}^{2}}{6}

σ^{2} = 80.2222

Standard Deviation

σ = 8.9567

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