From a sample with $n=24$, the mean number of televisions per household is 4 with a standard deviation of 1 television. Using Chebychev's Theorem, determine at least how many of the households have between 2 and 6 televisions.

Step 1 ：We are given a sample of 24 households, with the mean number of televisions per household being 4 and a standard deviation of 1 television.

Step 2 ：We want to determine at least how many of the households have between 2 and 6 televisions. This range is 2 standard deviations away from the mean (4 - 2 = 2 and 6 - 4 = 2).

Step 3 ：We can use Chebyshev's theorem, which states that at least 1 - 1/k^2 of the data within a dataset is within k standard deviations of the mean, where k is any positive integer greater than 1.

Step 4 ：In this case, we can use k = 2 in Chebyshev's theorem to find the minimum proportion of households that have between 2 and 6 televisions.

Step 5 ：Substituting k = 2 into the formula, we get a minimum proportion of 0.75.

Step 6 ：We then multiply this proportion by the total number of households (n = 24) to find the minimum number of households.

Step 7 ：Doing the calculation, we find that at least \(\boxed{18}\) households have between 2 and 6 televisions.