Section 3 Function: Examples
3.2 Function: Mean (AM, GM, HM)
- Calculate AM, GM and HM of a numeric vector using the following formula.
Arithmetic Mean (AM)
\[ \large AM = (x_1 + x_2 + ... + x_n)/n = \frac{1}{n}\sum\limits_{i=1}^{n} x_{i}\]
Geometric Mean (GM)
\[ \large GM = \sqrt[n]{(x_1 x_2 ... x_n)} = \left( \prod \limits_{i=1}^{n} x_{i} \right) ^{\frac{1}{n}} \]
Harmonic Mean (HM)
\[ \large HM = \frac{n}{(\frac{1}{x_1} + \frac{1}{x_2} + ... + \frac{1}{x_n})} = \frac{1}{\frac{1}{n}\sum\limits_{i=1}^{n} \frac{1}{x_i}}\]
3.3 Function: Variance & Standard Deviation
- Use the above data to calculate sample variance and standard deviation.
Sample Variance
\[ \large Var(x) = s_x^2 = \frac{1}{n-1}\sum\limits_{i=1}^{n} (x_i-\bar{x})^2 \]
Sample Standard Deviation
\[ \large s_x = \sqrt{s_x^2} = \sqrt{Var(x)} \]
3.4 Function: Summary Statistics
- Use base R functions or your own custom functions, write a function that will return a vector summary statistics of the following location and dispersion estimates of a numeric :
- Number of observations
- Number of non-missing observations
- Minimum value (Min)
- Maximum value (Max)
- Arithmetic mean (AM)
- Geometric mean (GM)
- Harmonic mean (HM)
- First quartile (Q1)
- Second quartile or Median (Q2)
- Third quartile (Q3)
- Range
- Interquartile range (IQR)
- Variance (Var)
- Standard deviation (SD)
- Coefficient of variation (CV)