Analysis Tasks
1. Provide the table including the summary statistics for days on the market and the standardized value for days on the market.
2. What do you notice when you compare the skewness and kurtosis of the original variables to the skewness and kurtosis of the standardized variables? Why do you think this happens?
3. provide a histogram of the days on the market for homes in the last year.
4. Provide the table including the summary statistics for days on the market with the observations outside of ±1.96 standard deviations of the mean removed.
5. What happened to the skewness once the extreme values were removed?
6. Provide the histogram of the number of days homes were on the market in the last year with the observations outside of ±1.96 standard deviations of the mean removed.
7. In a normal distribution, 95% of observations ±1.96 standard deviations of the mean. For this data set, what percentage of the original observations were retained after the observations outside of this range were removed?
8. After you standardized the filtered data, how many observations fell outside of the range of ±1.96 standard deviations of the mean? What percentage of the filtered sample fell within that range? Provide the Extreme Values table.
9. The North Valley Real Estate group provides a bonus for its representatives if a property is on the market for 14 days or less.
a. Using the original data set to two decimal places, what is the probability that one property would qualify an agent for this bonus?
b. Using the data set with the outliers removed, what is the probability that one property would qualify an agent for this bonus?
10. When an agent lists a property, the home needs to sell by the 15th day of the month for the commission to be on the next paycheck issues on the 1st of the following month.
a. What is the probability that a home listed on July 1st that did not sell in time to be included on the August 1st paycheck is sold by August 15th (there are 31 days in July), in time to be counted on the paycheck issued September 1 using the original data set?
b. What is the probability that a home listed on July 1st that did not sell in time to be included on the August 1st paycheck is sold by August 15th (there are 31 days in July), in time to be counted on the paycheck issued September 1, using the data set with the outliers removed?
1. In reviewing the mean, skew, percent of observations within ±1.96 standard deviations of the mean, and results from your probability calculations for your original data set and the data set with the outliers removed, comment on the use of the Empirical rule to identify outliers? (Do any outliers need to be removed? Should a different z value be selected?)
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