Statistics Frequency Distribution Problems Paper

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Statistics Assignment Question 1 The following shows the temperatures (high, low) and weather conditions in a given Sunday for some selected world cities. For the weather conditions, the following notations are used: c = clear; cl = cloudy; sh = showers; pc = partly cloudy. 1. Is “condition” an element, variable, or observation? 2. Provide the observation for Mexico City. 3. Give an example of a quantitative variable. 4. Provide the range for the low temperature. 5. What is the mode for the high temperature? 6. Explain why the "lo" is not ordinal. Question 2 A student has completed 20 courses in the School of Arts and Sciences. Her grades in the 20 courses are shown below. D D C D A B F A A A C B B C C D 1. Develop a frequency distribution table for her grades. 2. Create a bar chart for her grades. Remember the importance of good titles and labeled axes. 3. All the courses are three credits except for the two that are highlighted. They are science courses and are worth 5 credits each. Using a weighted mean, calculate the student's grade point average. A = 4.0; B= 3.0; C= 2.0; D =1.0; F = 0 Question 3 The number of hours worked per week for a sample of ten students is shown below. Student Hours 1 33 2 40 3 15 4 25 5 15 6 30 7 32 8 10 9 15 10 35 1. Determine the mean, median, and mode. 2. Explain which of the three values (mean, median, mode) is the best representation of central tendency in this particular set of data. (This is not an "in general" question it is based on the data of the assigment.) 3. What is the standard deviation for the number of hours worked? What does standard deviation tell us? 4. Create a histogram for this data. Discuss whether or not this data is normally distributed. Justify your answer. Question 4 You are given the following information on Events A, B, C, and D. P(A) = .5 P(B) = .3 P (C) = .20 P(A U D) = .8 P(A ∩ C) = 0.05 P (A │B) = 0.22 P (A ∩ D) = 0.25 1. Compute P(D). 2. Compute P(A ∩ B). 3. Compute P(A | C). 4. Compute the probability of the complement of C. 5. What does it mean to be mutually exclusive? Give an example. Question 5 When a particular machine is functioning properly, 80% of the items produced are non-defective. 1. If seven items are examined, what is the probability that three are defective? 2. If seven items are examined, what is the probability at at least three are non-defective? 3. If seven items are examined, what is the probability that at most, one is defective? 4. What is the expected number of defective items if ten items are examined? Question 6 The average starting salary of this year’s graduates of a large university (LU) is $34,000 with a standard deviation of $7,000. Furthermore, it is known that the starting salaries are normally distributed. 1. What is the probability that a randomly selected LU graduate will have a starting salary of at least $32,000? 2. Individuals with starting salaries of less than $19,900 receive a low income tax break. What percentage of the graduates will receive the tax break? 3. What percent of graduates will have their salaries one standard deviation from the mean? 4. What is the range of salaries that is one standard deviation from the mean? 5. What is the range of salaries that are two standard deviations from the mean? Question 7 A simple random sample of 8 computer programmers revealed the sex of the programmers and the following information about their weekly incomes. Programmer Weekly Income Sex A $550 M B $654 M C $911 F D $500 M E $727 M F $688 F G $1000 F H $892 M 1. If all the salaries were written on separate pieces of paper, and one was drawn at random, what is the probability that the one that was drawn would be over $700? 2. If a programmer were selected at random to complete a project, what would the probability be that the programmer was male? 3. What is the probability of selecting an income of under $700 per week given that a male was selected? 4. If all the salaries with the name of who earned it were written on separate pieces of paper and two were drawn at random (the first one was NOT returned to the pile), what is the probability that both were female? 5. If all the salaries with the name of who earned it were written on separate pieces of paper and two were drawn at random (the first one was NOT returned to the pile), what is the probability that the first draw would be the salary of a male and the second would be one of a female? Question 8 Students of a large university spend an average of $7 a day on lunch. The standard deviation of the expenditure is $2. A simple random sample of 25 students is taken. 1. What is the probability that the sample mean will be at least $4? 2. Jason spent $15 on his lunch. Explain, in terms of standard deviation, why his expenditure is not usual. 3. Explain what information is given on a z table. For example, if a student calculated a z value of 2.77, what is the four-digit number on the z table that corresponds with that value? What exactly is that 4-digit number telling us? 4. Explain why we use z formulas. Why don't we just leave the data alone? Why do we convert?
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Explanation & Answer

Attached.

Surname 1
Student’s Name
Institutional Affiliation
Instructor
Date
Statistics Assignment
Question 1
The following shows the temperatures (high, low) and weather conditions in a given Sunday for some
selected world cities. For the weather conditions, the following notations are used: c = clear; cl = cloudy;
sh = showers; pc = partly cloudy.

1. Is “condition” an element, variable, or observation?

Observation
2. Provide the observation for Mexico City.

In Mexico City when there is a showers the lowest temperature is 57 while the highest
temperature is 77.
3. Give an example of a quantitative variable.

Temparature data above is an example of quantative variable since they are found within
the form of both continuous and discrete data. For instance, high temperature
(99,92,77,72,88,78)
4. Provide the range for the low temperature.

The range of low temparture is in between 57-78
5. What is the mode for the high temperature?

Surname 2
The mode of high temperature is 77 since its value with highest frequency.
6. Explain why the "lo" is not ordinal.

Ordinal variables always take values that can be logically ranked and ordered, thus these
values can be rank lower or higher. Since low temaparature cannot be ranked as higher and
lower valus, “lo” is not ordinal
Question 2
A student has completed 20 courses in the School of Arts and Sciences. Her grades in the 20 courses are
shown below.
D

D

C

D

A

B

F

A

A

A

C

B

B

C

C

D

1. Develop a frequency distribution table for her grades.

Grade
A
B
C
D
F

Frequency
4
3
4
4
1

Cumulative frequency
4
7
11
15
16

2. Create a bar chart for her grades. Remember the importance of good titles and labeled axes.

A bar chart for a student

Surname 3

frequency
Grades
3. All the courses are three credits except for the two that are highlighted. They are science
courses and are worth 5 credits each. Using a weighted mean, calculate the student's grade
point average. A = 4.0; B= 3.0; C= 2.0; D =1.0; F = 0

Total points
A=4*4=16
B=3*2=6
C=4*2=8
D=3*1=3
F=1*0=0
Total pointes= 16+6+8+3+0= 33
Question 3
The number of hours worked per week for a sample of ten students is shown below.

Surname 4
Student

Hours

1

33

2

40

3

15

4

25

5

15

6

30

7

32

8

10

9

15

10

35

1. Determine the mean, median, and mode.
Mean

x=

x1 + x2 + ... + x10
10

x=

33 + 40 + 15 + 25 + 15 + 30 + 32 + 10 + 15 + 35
= 25
10

Median

Arrange in ascending order
10,15,15,15,25,30,32,33,35,40
Take 5th and 6th values since are considered as mid points then divide by 2
(25+30)/2=27.5
Mode

15 is the mode in above data since it is the most repeated value.
2. Explain which of the three values (mean, median, mode) is the best representation of central
tendency in this particular set of data. (This is not an "in general" question it is based on the
data of the assigment.)

Surname 5
The best representative of central of tendency in this particular set of data is mean because
the above type of data can be found as contious or discrete.
3. What is the standard deviation for the number of hours worked? What does standard deviation
tell us?
student

hours

( x − x)

( x − x) 2

1
2
3
4
5
6
7
8
9
10
Total

33
40
15
25
15
30
32
10
15
35
250

8
15
-10
0
-10
5
7
-15
-10
10

64
225
100
0
100
25
49
225
100
100
988

Sd =

(x − x )2
n −1

Sd =

988
= 10.5
9

The standard deviation tell us that there is 10.5 units of dispersion away from the mean.
4. Create a histogram for this data. Discuss whether or not this data is normally
distributed. Justify your answer.

Surname 6

The data above is not normally distributed since the line of symmetric does not lie in the
midst of the histogram. All data is more concentrated at the far away from the midst and
not along the midst.
Question 4
You are given the following information on Events A, B, C, and D.
P(A) = .5
P(B) = .3
P (C) = .20
P(A U D) = .8
P(A ∩ C) = 0.05

Surname 7
P (A │B) = 0.22
P (A ∩ D) = 0.25
...

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