Section 34 Review Examples


34.1 Example 1


  • Write an R expression and find the value of the following mathematical expressions:

\[ \large \frac{3^5}{3^2} \times \frac{2^5}{\sqrt[3]8} + \frac{5^3}{\sqrt{25}} - \frac{10+4}{7} \]

\[ \large \left(\frac{2^3}{4} + \frac{3^2}{4.5} \right) \left( \frac{10^2}{5+5} - \frac{10^3}{5\times\sqrt{25}} \right) \]


34.2 Example 2


  • Generate the following sequence of data and apply the functons:

    1 2 3 4 4 5 5 6 7 6 7 6 7 8 10 12 14

  • Name the vector as y

    • Hint: Use a combination of :, rep and seq
    • Apply the following function to y

    \[ \large \log_ey, \space \log_2y, \space \log_{10}y, \space log_5y \]

    \[ \large e^y, \space 2^y, \space 10^y \]


34.3 Example 3


  • Write a vector y of first 100 integer values.

  • Find the total counts of odd and even numbers in y.

  • Calculate the mean and median of y.

  • Check if 93 is a prime number

  • Check if 91 is a primer number

  • Check if the number 6451449 is divisible by 17


34.4 Example 4


  • Generate a vector of 20 random number x from the following Normal distribution:

\[ \large x \sim N(10,2^2) \]

  • Use R function to calculate mean, median, minimum, maximum, range, variance, standard deviation, standard error and coefficient of variation.

  • Use the following formula of Arithmetic Mean (AM), Geometric Mean (GM) and Harmonic Mean (HM)

\[ \large AM = (x_1 + x_2 + ... + x_n)/n = \frac{1}{n}\sum\limits_{i=1}^{n} x_{i}\]

\[ \large GM = \sqrt[n]{(x_1 x_2 ... x_n)} = \left( \prod \limits_{i=1}^{n} x_{i} \right) ^{\frac{1}{n}} \]

\[ \large HM = \frac{n}{(\frac{1}{x_1} + \frac{1}{x_2} + ... + \frac{1}{x_n})} = \frac{n}{\sum\limits_{i=1}^{n} \frac{1}{x_i}}\]


34.5 Example 5


  • Generate another vector of 20 random number y from the following Normal distribution:

\[ \large y \sim N(12,2^2) \]

  • Use R function to calculate mean, median, minimum, maximum, range, variance, standard deviation, standard error and coefficient of variation.

  • Use an appropriate R function to conduct a t-test to check the hypothesis if the mean of x is diffrent from the mean of y.

    • Hint: Explore the function t.test
    • Describe the results of the test