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
The computation should be carried out manually. All the steps that go into the computation should be presented and explained.
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 (True/False).______________________
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 you used).
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
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).
Value 0 1 2 3 4 5 6
Probability .10 .15 .25 .10 .10 .15
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 decimal places): _______________________________________________.
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 is:______.
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 (True/False)_________.
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: ______________________________.
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. I should treat the content of this file as the information from an entire population.
I need to save the file on my computer and read the data stored in the file into R.
19. Determine how many observations in the pop3.csv file are of type a: _______.
20. Using the appropriate R function with the default options, what is the median of the time column of pop3 (round to 3 decimal places): ______________________________.
21. What is the variance of the time column of pop3 (rounded to three decimal places)? _______
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