By R. A. Hill

The purpose of this ebook is to supply an basic therapy of the speculation of error-correcting codes, assuming not more than highschool arithmetic and the facility to hold out matrix mathematics. The publication is meant to function a self-contained path for moment or 3rd yr arithmetic undergraduates, or as a readable creation to the mathematical points of coding for college students in engineering or machine technological know-how.

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**Example text**

R will not perform arithmetic operations on objects containing NA, unless specifically mandated to skip/remove these missing values. rm (not available, remove) into the function. For the results data mean(results, n a . 78378 Notice that an NA message is returned for gender; this is because the gender variable is non-numeric and R cannot calculate its mean. 44 For females only, mean(marks[1:23]) [1] 6 5 . 25926 illustrating that the female average is substantially higher than the male average.

01) as an argument in the quantile function. 3 OVERALL SUMMARY STATISTICS A quicker way of summarizing the data is to use the summary function. summary(downtime) 18 SUMMARIZING STATISTICAL DATA Min. 00 1 s t Qu. 04 3 r d Qu. 50 Max. 00 which are the minimum, the first quartile, the median, the mean, the third quartile, and the maximum, respectively. An entire data frame may be summarized by using the summary command. Let us do this in the data frame results. First, it is wise to make a declaration about the categorical variable gender.

00 1 s t Qu. 3 0 . 78 3 r d Qu. 7 6 . 00 Max. 00 Notice how the display for gender is different from that for the other variables. We are simply given the frequency for each gender. For a separate analysis of archl, we might write mean(archl, n a . 56897 which is the average mark in Architecture in Semester 1. For more details, we could write summary(archl) which gives Min. 00 1st Qu. 57 3rd Qu. 25 Max. 4 PROGRAMMING IN R One of the great benefits of R is that it is possible to write your own programs and use them as functions in your analysis.