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The Chebychev's theorem states that for any numerical data set,
1.) at least
of the data lie within two standard deviations of the mean;
2.) <span> at least </span><span><span>
of the data lie within three standard deviations of the mean</span>;
3.) at least </span><span><span>
of the data lie within k standard deviations of the mean,</span> where k is any positive whole number that is greater than 1.</span>
Thus, given a data set with a mean of 150 and a standard Deviation of 15, 75% of the data represent of the data, and according to Chebychev's theorem, <span>at least of the data lie within two standard deviations of the mean.
Thus, 75% of the data will fall within the interval
.
Therefore, 75% of the data will fall within the interval 120 to 180.</span>
1.) at least
2.) <span> at least </span><span><span>
3.) at least </span><span><span>
Thus, given a data set with a mean of 150 and a standard Deviation of 15, 75% of the data represent
Thus, 75% of the data will fall within the interval
Therefore, 75% of the data will fall within the interval 120 to 180.</span>