QS381: Introduction to Probability and Statistics

Problem set #2

[Note: #1-and #2 are to be done by hand. However, for #2, you are encouraged to use MINITAB or EXCEL to generate sum and sum of squares of the grass data. The final statistics (such as mean, variance etc) should be done by hand.}

 

In goodall (for undergrads) and mead (for grads), copy the data file ‘grass.DAT from my directory using the command:

 

cp ~krishna/grass.DAT .

Do not forget to insert space and period after DAT. This command will create a copy of my file grass.DAT into your directory under the same name. The data consists of 120 observations in one column.

This data set (from Freund: Ex 2.42, p 29) consists of the crested wheatgrass root penetration in feet after one month. Read this file into MINITAB or EXCEL storing the data in the first column.

 

  1. Compute the absolute and relative frequencies of the root penetration after grouping them in the classes 0.50-0.59, 0.60-0.69, …, 1.40-1.49.

Draw histogram, frequency polygon and ogive of the frequency data showing both absolute and relative frequencies. Show the join points for all graphs along the X-axis.

 

 

 

#2. Calculate the arithmetic mean, variance, standard deviation and coefficient of variation of the root penetration for the ungrouped and grouped data.

Using the raw data, determine the percent of observations within:

(Arithmetic mean) ± k*(standard deviation)

For k = 1.5, 2, and 3.How good is Tchebysheff's theorem vis-a-vis empirical rule in predicting these percentages?

 

#3. Using the data and appropriate MINITAB or EXCEL commands compute the mean and standard deviation to verify the results obtained in #2.