Question

Calculate the standard deviation from the
following data.
14 22 9 15 20 17 12 11

Answer 1

Answer:

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Answer 2

Answer:

Standard deviation of the given data = 2√5

Step-by-step explanation:

Given:- The given data is 14 22 9 15 20 17 12 11.

To Find:- Standard deviation of the data.

Solution:-

Let's arrange the given data in descending order, we get

22, 20, 17, 15, 14, 12, 11, 9

Mean of the data = (9 + 11 + 12 + 14 + 15 + 17 + 20 + 22)/8

                             = (20+26+32+42 ) / 8

                             = ( 46 + 74 )/8

                             = 120/8

                             = 15.

We know that SD = ∑ $\sqrt{\frac{(x_{i} - mean )^{2}}{n-1} }$  for i = 1 to i = n.

∴ SD = $\sqrt{\frac{(9-15)^{2}+(11-15)^{2}+(12-15)^{2}+(14-15)^{2}+(15-15)^{2}+(17-15)^{2}+(20-15)^{2}+(22-15)^{2}}{8-1} }$

        = √ ( (36 + 16 + 9 + 1 + 0 + 4 + 25 + 49) / 7 )

        = √ ( 140 / 7)

        = √20

        = √ 2² . 5

        = 2√5

Therefore, standard deviation of the given data = 2√5

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