27 Aug statistic homework
Q1. The file \Files\Homework Materials\Census.xlsx shows a portion of median household income (income in $) and median house value (house Value in $) for the 50% in 2010.
1. Construct a boxplot for household income and use it to identify outliers, if any, and comment on skewness.
2. Construct a boxplot for median house value and use it to identify outliers, if any, and comment on skewness.
3. Identify outliers using z-score. That is, identify data points that have a z-score greater than 3 or less than -3.
4. Calculate the coefficient of variation for Foreign Born % and No HS Diploma %. Which measures exhibit greater relative dispersion?
Q2. The following table shows the annual returns (in%) for the Fidelity South Asia Fund and the Fidelity Canada Fund for 2005 through 2009.
| Year | South Asia | Canada |
| 2005 | 43.71 | 35.02 |
| 2006 | 44.33 | 25.04 |
| 2007 | 55.17 | 42.64 |
| 2008 | -56.64 | -39.63 |
| 2009 | 11.60 | 27.89 |
1. which fund had the higher average return?
2. Which fund was riskier over this time period?
3. Given a risk-free rate of 3%, which fund has the higher Sharpe ratio? What does this ratio imply?
Q3. A sample of the salaries of data analysts at a local technology park revealed a mean income of $72,000 with a standard deviation of $3,000.
1. Using Chebyshev’s theorem, what percentage of the analysts earns at least $63,000 but no more than $81,000?
2. Assume that salaries follow a bell-shape distribution. Using the empirical rule, what percentage of the analysts earns at least $66,000 but no more than $78,000?
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