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bekas
7 days ago
14

Find the standard deviation of the following data. Answers are rounded to the nearest tenth. 5, 5, 6, 12, 13, 26, 37, 49, 51, 56

, 56, 84
Mathematics
1 answer:
Inessa [12.5K]7 days ago
6 0

Response:

24.2 (rounded to the nearest tenth)

Detailed breakdown:

The data type involved is ungrouped

standard deviation =√ [∑ (x-μ)² / n]

average (μ)=∑x/n

           = \frac{5+5+6+12+13+26+37+49+51+56+56+84}{12}

          =33.3

For the values 5, 5, 6, 12, 13, 26, 37, 49, 51, 56, 56, 84, the x-μ results will be

                   -28.3, -28.3, -27.3, -21.3, -7.3, 3.7, 15.7,17.7, 22.7,22.7,50.7

Calculating (x-μ)² gives: 800.89, 800.89, 745.29, 453.69, 53.29, 13.69, 246.49, 313.29, 515.29, 515.29, 2570.49

Then, ∑ (x-μ)² results in = 7028.59

Thus, standard deviation = √(7028.59 / 12)

                      =24.2

     

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Which formula can be used to describe the sequence? -2/3,-4,-24,-144...
lawyer [12517]

The formula that describes the sequence is a_{n}=\frac{-2}{3}(6)^{n-1}

Step-by-step explanation:

The nth-term formula for a geometric sequence is a_{n}=a(r)^{n-1}, where

  • a represents the first term of the sequence
  • r signifies the common ratio between any two consecutive terms
  • r=\frac{a_{2}}{a_{1}} = \frac{a_{3}}{a_{2}}

∵ The sequence is \frac{-2}{3}, -4, -24, -144,.......

∵ The first term is \frac{-2}{3}

∵ The second term is -4

∴ \frac{-4}{\frac{-2}{3}}=6

∵ The third term is -24

∴ \frac{-24}{-4}=6

∵ The fourth term is -144

∴ \frac{-144}{-24}=6

∵  \frac{a_{2}}{a_{1}} = \frac{a_{3}}{a_{2}} =  \frac{a_{4}}{a_{3}} = 6

∴ There is a consistent ratio between two consecutive terms

∴ The sequence qualifies as a geometric sequence

∵ The formula for the nth term of the geometric sequence is a_{n}=a(r)^{n-1}

∵ a = \frac{-2}{3}

∵ r = 6

∴ The equation for the sequence is a_{n}=\frac{-2}{3}(6)^{n-1}

The formula that can be employed to outline the sequence is a_{n}=\frac{-2}{3}(6)^{n-1}

Learn more:

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Answer:

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Step-by-step explanation:

It is understood that

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It is also known that

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