Chebyshev's Theorem Calculator
Answer:
55.56%
For any shaped distribution, at least 55.56% of the data values will lie within 1.5 standard deviation(s) from the mean. That is, from 1.5 standard deviations below the mean to 1.5 standard deviations above the mean.
Solution:
To apply Chebyshev's Theorem, use the formula below. The number of standard deviations away from the mean is symbolized by $k$. $$ 1 - \frac{1}{k^2} $$
Substituting the number of standard deviations, 1.5 for k, we have: $$ 1 - \frac{1}{1.5^2} $$
1. Square the value for k. We have: $$ k^2 = 1.5^2 = 2.25 $$
2. Next, divide 1 by the answer from step 1 above: $$ \frac{1}{2.25} = 0.44444444444444 $$
3. Subtract the answer in step 2 above from the number 1: $$ 1 - 0.44444444444444 $$ $$ = 0.55555555555556$$
4. Multiply by 100 to get the percent. Here, we round to at most 2 decimal places. $$ = 55.56\% $$