Sampling distributions
The Empirical rule tells more about the distribution in a bell shaped. Since the information about predictions in the graph is a large data, Empirical rule provides that percentages are of higher prediction than the Chebyshev’s theorem. In addition, it defines that 68% of the observation roughly selected is expected to fall within 10 of the mean and 95% should follow within 10 of the mean and finally 99.3% of the value of the data selected should fall 10 from the mean, (Black, 2012).
From the real estate data provided, empirical formula dictates 2 standard deviations fall on a 95% data distribution. Here, it is applicable to use the Empirical rule because the intervals specified are greater or less than the ones given in the rule.
From the question, since the interval from 380,000 to 465500 is;
(2.5-1.5) =1, by Empirical rule provides that most of the listing price should fall in 68%.
Therefore, the percentage by Empirical formula will be 68% because most of the price listing that fall under a standard deviation of mean and interval of 2 fall under this estimation value. My sample means clearly conforms to the Empirical rule which states that for normal distribution, nearly of data will fall in three standards of mean.
On the other hand, Chebyshev’s theorem provides that regardless of the order in distribution, the probability that the provided data selected randomly is at least
[ 100 (1-1/k^2)] 100%
This rule does not limit the set of data. However, the real estate data shows that 3/4 of the listing, which are different, lie under a standard deviation mean with an interval of x-±2. Chebyshev helps in estimating values or data which is symmetrical about the mean. It is preferably used because it works well for all data regardless of order and for that case, in different price listing values.
Reference
Top of Form
Black, K. (2012). Business statistics: For contemporary decision making. Hoboken, NJ: Wiley.