Assignment Title
Sampling Distributions – Real Estate
In the analyzed data sample, population mean and standard deviation were found. They are presented in Tab.1:
Mean is the most common measure of central tendency in data. It shows the central value of the set of data and is found a s an arithmetic mean. For population, all values are summed up and divided by the number of values. In this population, the central value is $286,946 – it is the average listing price of the 100 houses.
Standard deviation is a measure of dispersion of the data. In the population, it shows the overall pattern of the distribution. Standard deviation indicates how spread out is the data around the mean. It is found by calculating each data point’s distance to the mean, finding the mean of these distances, and taking square root out of this value. In this population, the standard deviation of the whole population is $258,188. Based on this value we form our expectations of how probable it is to find an observation with a given price. If the distribution is approximately normal, the so-called empirical rule can be used to make these predictions. This rule states that if the distribution is approximately normal then about 68% of data values are found within one standard deviation from the mane. It means that 68% prices should be found within the interval $28,758 - $545,133. Around 95% percent of data values should be found within two standard deviations from the mean, which for these data is -$229,430 - $803,321. And around 99.7% of observations lie within three standard deviations from the mean. For these data this interval is -$487,618 - $1,061,509.
If the population is broken down into 10 samples of n = 10, the mean for each sample can be found. They are listed in the Tab. 2:
Table 2. Sample Means
