Part A: Multiple Choice
Using the following information to answer questions 1-8:
1. What is the mean?
a) 1.90 b) 2.11 c) 1.73 d) 1.66
2. What is the median?
a) 1.00 b) 1.50 c) 1.60 d) 1.90
3. What is the mode?
a) 0 b) 1 c) 2 d) 3
4. What is the range?
a) 1 b) 4 c) 5 d) 3
5. What is the variance?
a) 1.66 b) 2.77 c) 1.76 d) 3.11
6. What is the standard deviation?
a) 1.66 b) 2.77 c) 1.76 d) 3.11
7. What is the 1st quartile?
a) 0 b) 1 c) 2 d) 3
8. What is the 70th percentile?
a) 1 b) 1.5 c) 2 d) 2.5
Questions 9-16 refer to the following frequency distribution:
The following information represents the number of tons of grain stored at the 60 grain elevators of central Soya, Inc.
| Class |
Frequency |
| 160-164 |
6 |
| 165-169 |
14 |
| 170-174 |
16 |
| 175-179 |
13 |
| 180-184 |
11 |
| Total |
60 |
9. What is the relative frequency for the class 170-174?
a) 16 b) 36 c) 0.27 d) 0.60
10. What is the mean?
a) 170.25 b) 12 c) 172.75 d) 167
11. What is the median?
a) 169.5 b) 170 c) 172.63 d) 173.13
12. What is the mode?
a) 16 b) 170 c) 172 d) 174
13. What is the variance?
a) 39.68 b) 12.33 c) 151.55 d) 149.02
14. What is the standard deviation?
a) 6.30 b) 3.51 c) 12.31 d) 12.21
15. What is the 1st quartile?
a) 168.21 b) 167.07 c) 167.57 d) 167.71
16. What is the 70th percentile?
a) 176.35 b) 176.85 c) 176.81 d) 177.31
Part B: True or False
17. The random sample is the most important, because statistical theory applies to it alone.
18. In a frequency distribution, the class mark is the number of observations that fall within that class.
19. Original class interval frequencies can be obtained by multiplying the respective relative frequencies by the total number of observations.
20. The sum of the class frequencies is equal to the number of observations made.
21. A relative frequency distribution describes the proportion of data values that fall within each category.
22. There would be no need for statistical theory if census, rather than a sample was always used to obtain information about populations.
23. The arithmetic mean is the sum of the data values divided by the number of observations.
24. P(A ∩ B) is P(B|A) *P(A)
25. The median always exists in a set of numerical data.
26. (A ∩ B) = 0 means that A and B are mutually exclusive events.
27. Mutually exclusive events imply that if one event occurs, the other cannot occur. An event (e.g.,A') and its complement are always mutually exclusive.
28. P(A) + P(A') = 1
29. Events are independent when the occurrence of one event has no effect on the probability that another will occur.
30. The P(x) is always 0 ≤ P(x) ≤ 1.
Part C: Answer the following questions
31. Name 3 types of statistical samples
32. Name reasons why we use samples instead of an entire population
33. Name types of random samples.
34. Name the measure of central tendency.
35. Name measures of spread or variability.
36. Show that you understand the difference between a sampling error and a sampling bias.
37. Name 4 parts of the regression.
38. When do we use the regression?
39. Explain the concept of error and uncertainty as it relates to decision making.
Part D: (40-50)
40. Train A and Train B are two transportations that people can use to transport from Boston to New York. Sample of times recorded in minutes for each train are shown below.
| Train A |
28 |
29 |
32 |
37 |
33 |
25 |
29 |
32 |
41 |
34 |
| Train B |
29 |
31 |
33 |
32 |
34 |
30 |
31 |
32 |
35 |
33 |
Please answer the following questions.
Train A
a) Mean
b) Median
c) Variance
d) Standard deviation
Train B
e) Mean
f) Median
g) Variance
h) Standard deviation
i) From above computed results from Train A and Train B, what train should be preferred and why?