warpbreaks is a built-in R data.frame which gives the number of warp breaks per loom, where a loom corresponds to a fixed length of yarn. We are interested in some descriptive statistics related to the breaks column of the warpbreaks data.frame. We can access this data directly by using the assignment x <- warpbreaks$breaks (In R, use ? warpbreaks for info on this data) The values of x if assigned as above are: [1] 26, 30, 54, 25, 70, 52, 51, 26, 67, 18, 21, 29, 17, 12, 18, 35, 30 [18] 36, 36, 21, 24, 18, 10, 43, 28, 15, 26, 27, 14, 29, 19, 29, 31, 41 [35] 20, 44, 42, 26, 19, 16, 39, 28, 21, 39, 29, 20, 21, 24, 17, 13, 15 [52] 15, 16, 28 You should get these values from the R assignment above rather than manually entering the data. a.Calculate the maximum value of x b. Calculate the interquartile range of x using the R, IQR function. c. Calculate the sample range of x. (one number) d. Calculate the sum of the square roots of the elements of x e. Calculate the sample mean of x. f. Calculate the sample variance of x. g. Calculate the sample standard deviation of x. h. What proportion of the x values are more than 1 sample standard deviation from the sample mean 0.778 i. Calculate the sample median of x. j. How many times does the sample median of x appear? k. How many of the elements of x are smaller than the sample mean of x? 33

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warpbreaks is a built-in R data.frame which gives the number of warp breaks per loom, where a loom corresponds to a fixed length of yarn. We are interested in some descriptive statistics related to the breaks column of the
warpbreaks data.frame. We can access this data directly by using the assignment
x <- warpbreaks$breaks
(In R, use ? warpbreaks for info on this data)
The values of x if assigned as above are:
[1] 26, 30, 54, 25, 70, 52, 51, 26, 67, 18, 21, 29, 17, 12, 18, 35, 30
[18] 36, 36, 21, 24, 18, 10, 43, 28, 15, 26, 27, 14, 29, 19, 29, 31, 41
[35] 20, 44, 42, 26, 19, 16, 39, 28, 21, 39, 29, 20, 21, 24, 17, 13, 15
[52] 15, 16, 28
You should get these values from the R assignment above rather than manually entering the data.
a.Calculate the maximum value of x
b. Calculate the interquartile range of x using the R, IQR function.
c. Calculate the sample range of x. (one number)
d. Calculate the sum of the square roots of the elements of x
e. Calculate the sample mean of x.
f. Calculate the sample variance of x.
g. Calculate the sample standard deviation of x.
h. What proportion of the x values are more than 1 sample standard deviation from the sample mean 0.778
i. Calculate the sample median of x.
j. How many times does the sample median of x appear?
k. How many of the elements of x are smaller than the sample mean of x? 33
Transcribed Image Text:warpbreaks is a built-in R data.frame which gives the number of warp breaks per loom, where a loom corresponds to a fixed length of yarn. We are interested in some descriptive statistics related to the breaks column of the warpbreaks data.frame. We can access this data directly by using the assignment x <- warpbreaks$breaks (In R, use ? warpbreaks for info on this data) The values of x if assigned as above are: [1] 26, 30, 54, 25, 70, 52, 51, 26, 67, 18, 21, 29, 17, 12, 18, 35, 30 [18] 36, 36, 21, 24, 18, 10, 43, 28, 15, 26, 27, 14, 29, 19, 29, 31, 41 [35] 20, 44, 42, 26, 19, 16, 39, 28, 21, 39, 29, 20, 21, 24, 17, 13, 15 [52] 15, 16, 28 You should get these values from the R assignment above rather than manually entering the data. a.Calculate the maximum value of x b. Calculate the interquartile range of x using the R, IQR function. c. Calculate the sample range of x. (one number) d. Calculate the sum of the square roots of the elements of x e. Calculate the sample mean of x. f. Calculate the sample variance of x. g. Calculate the sample standard deviation of x. h. What proportion of the x values are more than 1 sample standard deviation from the sample mean 0.778 i. Calculate the sample median of x. j. How many times does the sample median of x appear? k. How many of the elements of x are smaller than the sample mean of x? 33
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