The mean time in the finals for the womens 800meter freestyl

The mean time in the finals for the women\'s 800-meter freestyle at the 2012 Summer Olympics was 502.84 seconds, with a standard deviation of 4.68 seconds. Apply Chebychev\'s Theorem to the data set using k=2. Interpret the results

Solution

Solution:

Chebychev\'s theorum states that the proportion of data lying within K standard deviations of the mean is always at least
1 - 1/K^2 where K is greater than 1. So to apply that to your problem, insert 2 for K in the equation and solve:

1 - 1/2^2 = 1 - 1/4 = 3/4

That means that at least 3/4 or 75% of the times will lie within 2 standard deviations of the mean. To figure out what times form this 75% boundary, just subtract two standard deviations from the mean for the lower boundary and add two standard deviations to the mean for the upper boundary.

step 1:

Subtract two standard deviations from the mean.

given mean= 502.84 seconds

sd=standard deviation=4.68 seconds

mean-2sd=502.84 -2(4.68)= 493.48 seconds

Step2:

Add two standard deviations to the mean

mean+2sd=502.84 +2(4.68)=512.2 seconds

Interpretation:

By Chebychev’s Theorem, you can say that at least 75% of the times the mean time is in between

493.48 and 512.2 seconds.