For Tasks 1-8, consider the following data:
7.2, 1.2, 1.8, 2.8, 18, -1.9, -0.1, -1.5, 13.0, 3.2, -1.1,
7.0, 0.5, 3.9, 2.1, 4.1, 6.5
In Tasks 1-8 you are asked to conduct some computations
regarding this data. The computation should be carried out
manually. All the steps that go into the computation should be
presented and explained. (You may use R in order to verify your
computation, but not as a substitute for conducting the manual
A Random Variable
In Tasks 9-18 you are asked to conduct some computations
regarding a random variable. Use the (incomplete) table below as
the definition of this random variable (after you fill in the
blank). The sample space of a random variable is comprised of the
integers 0, 1, 2, 3, 4, 5, and 6. The probabilities of each value
are shown in the table below (with one missing value).
For Tasks 19-21, use the file called "pop3.csv" found here.
That file contains information about time to failure of an entire
production of some computer parts. The file contains two variables,
"type" and "time", each measured over the 100,000 members of the
population. The variable "type" is a factor, with three levels,
"a", "b" and "c", and the variable "time" is numeric. If the value
of time is 4, that means that the part lasted 4 units of time
(years?) before a failure occurred. You should treat the content of
this file as the information from an entire population.
Save the file on your computer and read the data stored in the
file into R. If you have trouble loading the data into R, email
your instructor immediately—don't worry if you think you will find
the answer 1 minute after sending the email—just send the email.
Tasks 19-21 refer to the information in the file.
Submitting the Assignment
For the assignment you should complete the following tasks.
Tasks 1-8 refer to the sequence of 17 data values presented above,
Tasks 9-18 refer to the random variable and Tasks 19-XXX21 refer to
the information of a population of computer parts that is stored in
the file "pop3.csv". Your answers should be short and clear.
We recommend that you copy and paste the tasks below into the
assignment submission area. You can then write your answers to the
tasks in the designated positions that are marked in the
1. Using the list of 17 numbers at the top of the page, the
median of this data, rounded to two decimal places, is:_____.
2. If you find the median using the original method (paper and
pencil), you have to arrange the values into numeric order
3. The interquartile range for this data is (round each value
to 3 decimal places):_______.
4. The formula for calculating the interquartile range
is_____________ (show the formula and a citation to the source that
5. Using techniques that we have studied in this course, the
upper and lower cutoff points (rounded to three decimal places) for
identifying outliers (in the given data sample) are: ________ and
________ (this is not a request to show any outliers--just the
cutoff points that would determine what constitutes an outlier).
You may round to three decimal places.
6. The summary() command shows a list of outliers, if there
are any (True/False):______________________
7. The list of outlier values is:_____________ (if there are
none, write "NA").
8. The standard deviation of the list of 17 numbers is (round
to 3 decimal places): ______________
A Random Variable:
9. The missing probability value (under the number 4) in the
random variable table above is:_______
10. The sum of the probabilites in the second row of any
random variable table like the one above should equal (round to 3
11. Read section 4.4.1 in the book (Yakir, 2011). Do the
numbers in the table above (for the random variable) represent a
data sample (Yes/No)?____
12. In the random variable table shown above, the value in the
second row represents the cumulative probability of the
corresponding values in the first row (True/False) _________
13. The probability that a randomly selected value from this
random value will be less than or equal to 3 is :_____.
14. What is the probability that a randomly selected value
from the random variable would be exactly 1.5? ___________ .
15. Review section 4.4 in the book (Yakir, 2011), especially
pages 57—58. The expectation of the random variable
16. To find the expectation of a random variable by using a
relative frequency table, you can add the values in the first row
of the table and divide by the number of columns in the table
17. Study Yakir (2011) pp. 57-59 and solved problems
4.1.6-4.1.8. The (population) standard deviation of the random
variable above is (round to 3 decimal places):_______ (hint, you
can not put values from the table into the sd() function because
the sd() function does not adjust for the probabilities).
18. If you have already calculated the standard deviation of a
data sample, what is the next thing to do to find the variance:
19. Determine how many observations in the pop3.csv file are
of type a: _______.
20. Using the appropriate R function with the defaul options,
what is the median of the time column of pop3 (round to 3 decimal
21. What is the variance of the time column of pop3 (rounded
to three decimal places)? _______