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andreyandreev [35.5K]
3 years ago
7

for the following data set calculate the percentage of data points that fall within one standard deviation of the mean, and comp

are the result to the expected percentage of a normal distribution. {50,46,54,51,29,52,48,54,47,48}
Mathematics
1 answer:
gayaneshka [121]3 years ago
3 0

Answer:

First we need to find the mean and standard deviation of the given data.

The mean and standard deviation are given below:

Mean=\frac{50+46+54+51+29+52+48+54+47+48}{10}=\frac{479}{10}=47.9

Standard-deviation=\sqrt{\frac{\sum(x-\bar{x})^2}{n-1} }

                             =\sqrt{\frac{(50-47.9)^2+(46-47.9)^2+(54-47.9)^2+...+(48-47.9)^2}{10-1} }

                             =7.20

We have:

\bar{x} \pm s=(47.9 \pm 7.20)

                     =(47.9-7.20, 47.9+7.20)

                     =(40.7, 55.1)      

Therefore, the percentage of values that lies within one standard deviation of the mean is:

\frac{9}{10} \times 100 =90\%

The expected percentage of values within one standard deviation of the mean according to normal distribution is 68%.

Therefore, the observed percentage of values within one standard deviation of the mean is much higher than the expected percentage of a normal distribution.

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