Question

The temperature in a certain location was recorded each day for two months. The mean temperature was 28.8°F with a standard deviation 7.4°F. What can you determine about these data by using Chebyshev's Inequality with =K3?

Answer 1

Chebyshev's inequality states that for any given dataset, at least 1 - 1/k^2 of the data will lie within k standard deviations from the mean.

When k = 3, at least 1 - 1/3^2 = 1 - 1/9 = 8/9 of the data will lie within 3 standard deviations from the mean.

So, for the temperature data, we can determine that at least 8/9 of the data will lie between 28.8 - 3 × 7.4 = 7°F and 28.8 + 3 × 7.4 = 50.6°F.

In other words, we can say that at least 8/9 of the temperatures recorded during the two months were between 7°F and 50.6°F.