You are conducting a survey on the number of pets per...

You are conducting a survey on the number of pets per household in your region. From a sample with $n=40,$ the mean number of pets per household is 2 pets and the standard deviation is 1 pet. Using Chebychev's Theorem, determine at least how many of the households have
0 to 4 pets.

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Key Concepts

Chebyshev's Theorem

Chebyshev's Theorem is a statistical principle that provides a lower bound on the proportion of observations within a certain number of standard deviations from the mean, regardless of the data's distribution. It states that for any k > 1, at least 1 - 1/k² of the data lies within k standard deviations of the mean. This theorem is especially useful when the distribution is unknown or not normal.

Mean

The mean is the arithmetic average of a set of values and serves as a measure of central tendency in a dataset. In the context of statistical surveys and analyses, the mean is used to summarize the typical value observed, around which other measurements may cluster.

Standard Deviation

Standard deviation is a measure of the dispersion or spread of a set of data points around the mean. It quantifies the amount of variation or variability in the dataset and is crucial for determining intervals (such as those calculated using Chebyshev's Theorem) that capture a specified proportion of the data.

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