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The following data are the result of a historical study of the number of flaws found in a porcelain cup produced by a manufacturing firm.

Flaws Probability
0
0.451
1
0.270
2
0.134
3 0.078
4 0.038

What is the standard deviation value?


Round the intermediate values to 6 decimal places. Round your answer to 4 decimal places.

Sagot :

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Flaws                        Probability

0                                0.451

1                                 0.270

2                                0.134

3                                0.078

4                                0.038

The mean or expected value is:

E ( X ) = μ = ∑ x P ( x )

µ = 0.00000

     0.27000

     0.26800

     0.23400

     0.15200

(x - µ)2 = 0.00000

              0.26645

              1.499912

              3.825378

              7.403552

(x - µ)2 . P(x) = 0.000000

                       0.071941

                       0.200988

                       0.298379

                       0.281334

The Standard Deviation value is :

(x - µ)2 . P(x) - µ

0.852582 - 0.924000

-0.0714

A Standard Deviation (or σ) is a measure of ways dispersed the facts is on the subject of the mean. Low standard deviation way statistics are clustered around the imply, and excessive standard deviation shows data are extra unfold out.

What is a good standard deviation?

The empirical rule, or the sixty eight-ninety five-99.7 rule, tells you wherein maximum of the values lie in a normal distribution: round 68% of values are inside 1 widespread deviation of the mean. round 95% of values are inside 2 widespread deviations of the imply. Around 99.7% of values are within 3 well known deviations of the imply.

How do  if a Standard Deviation is high or low?

One manner to decide if a Standard Deviation is excessive is to evaluate it to the mean of the dataset. A coefficient of variation, frequently abbreviated as CV, is a way to measure how unfold out values are in a dataset relative to the imply.

Learn more about Standard Deviation here:- https://brainly.com/question/475676

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