Question

601 complete) This Test According to Chebyshe's Theorem, what is the percentage of sample data that is within 2 standard deviations of the mean? What is the actual percentage of the sample data below that is within 2 standard deviations of the mean? 45 5 7 3 6 7 5 1 6 57 3 53 8 4 2 4 4 According to Chebysher's Theorem, O A atleast 60% of sample data is within 2 standard deviations of the mean OB. at least 80% of sample data is within 2 standard deviations of the mean OC. at least 96% of sample data is within 2 standard deviations of the man OD. at least 75% of sample data is within 2 standard deviations of the mean The actual percentage for the given sample data is O A 100% OB. 75% Click to select your answer Type here to O BI e ENPM 7/21/2000 4 6 5 3 8 7 2 9 P W O R. T Y m

Answer 1

According to Chebyshev's Theorem, for k=2, we can say that 75% of data lies within 2 standard deviations.

Option D is correct.

From the data we have,

Here number of samples = n = 20

$\small \overline x=\frac{1}{n}\sum x_i=\frac{1}{20}[45+5+...+4+4]=11.8$

$\small s=\sqrt{\frac{1}{n-1}\sum (x_i-\overline{x})^2}$

   

1 [45 - 11.852 + (5-11.8) +..+ (4-11.8)] = 17.39 20-1

$\small \overline{x}-2s=11.8-2\times 17.39=-22.98$

$\small \overline{x}+2s=11.8+2\times 17.39=46.58$

We can see that, 18 out of 20 = 90% for the given sample data is between 2 standard deviations from the mean.