Question: Consider the following grouped data frequency distribution where \(x_{i}\) and \(f_{i}\) are the \(i^{\text {th }}\) observation and frequency, respectively:

We know that \(\sum_{i=1}^{5} f_{i} x_{i}=55\) and \(\sum_{i=1}^{5} f_{i} x_{i}^{2}=375\). Given the above information, is it possible to find values of \(f_{3}\) and \(f_{4} ?\) If so, explain how to calculate them. Then, answer the following questions:

1. Calculate the mean, median, and mode.
2. Calculate the geometric and harmonic mean.
3. Is the distribution symmetrical or non-symmetrical? Why? Why not?
4. Calculate variance, standard deviation, mean deviation and coefficient of variation.
5. Calculate the Pearson's and software coefficients of skewness.
6. Calculate \(15^{\text {th }}\) percentile, \(3^{\text {rd }}\) quartile, and \(4^{\text {th }}\) decile.
7. Does Empirical Rule work here? Why? Why not?
8. Does Chebyshev's Theorem work here? Why? Why not?

Price: $2.99

Solution: The downloadable solution consists of 4 pages
Deliverable: Word Document