This document is a 10 page course worksheet for a probabilities and statistics class. It contains 9 problems involving constructing various statistical distributions such as frequency, relative frequency, and percent frequency distributions from sample data. It asks students to calculate measures of central tendency and dispersion like mean, median, mode, range, and standard deviation. Students are also asked to create graphs like histograms, box plots, and dot plots to visualize the data. The worksheet provides sample data and guides students through completing tables and selecting the right statistical values or conclusions.

1. Northern Border University
College of engineering
Industrial Engineering Department
Year : 2020-2021,1st
Term
Course : Probabilities and. Statistics
Course No.: 1405 -204
Sheet No. 1
Dr. Yehya Mesalam
Page 1 of 10
1. Thirty students are completed probability course in the first year of mechanical engineering
department. Their grades are shown below.
B B A F C C
C C B D B DN
B DN F A D D
F B C D A F
DN B DN B A B
(a) Develop a frequency distribution for their grades.
(b) Develop a relative frequency distribution for their grades.
(c) Develop a percent frequency distribution for their grades.
(d) Develop a bar graph.
(e) Construct a pie chart

2. Northern Border University
College of engineering
Industrial Engineering Department
Year : 2020-2021,1st
Term
Course : Probabilities and. Statistics
Course No.: 1405 -204
Sheet No. 1
Dr. Yehya Mesalam
Page 2 of 10
2. The following measurements were recorded for the cooking time, in hours, of a certain type of
Meat
3.6 2.5 4.8 4.9 3.6
2.9 3.4 5.6 3.7 2.8
4.4 4.0 5.2 3.0 4.8
4.8 4.0 5.9 6.5 4.8
Assume that the measurements are a simple random sample.
(a) What is the sample size for the above sample?
(b) Calculate the sample mean for these data.
(c) Calculate the sample median.
(d) Plot the data by way of a dot plot.

3. Northern Border University
College of engineering
Industrial Engineering Department
Year : 2020-2021,1st
Term
Course : Probabilities and. Statistics
Course No.: 1405 -204
Sheet No. 1
Dr. Yehya Mesalam
Page 3 of 10
3. Construct a stem-and-leaf display for the following data, Then calculate the mean, mode, and
median, for the following data
10.7 4.9 8.9 11.7 6.3 7.7 3.3 4.9 8.3 10.2 11.9
7.7 8.9 6.4 6.3 7.7 3.9 4.9 8.9 10.6 10.9 4.9
8.9 11.7 9.3 7.3 10.3 4.9 8.7 10. 4 7.4 6.9 4.2

4. Northern Border University
College of engineering
Industrial Engineering Department
Year : 2020-2021,1st
Term
Course : Probabilities and. Statistics
Course No.: 1405 -204
Sheet No. 1
Dr. Yehya Mesalam
Page 4 of 10
4. The following are historical data on staff salaries (dollars per hour) for 30 schools sampled in
the eastern part of the United States in the early 1970s.
3.79 2.99 2.77 2.91 3.10 1.84 2.52 3.22 3.14 2.68
2.45 2.14 2.67 2.52 2.71 2.75 3.57 3.85 3.54 3.51
3.36 2.05 2.89 2.83 3.13 2.44 2.10 3.71 2.37 3.37
(a) Compute the sample mean and sample standard deviation.
(b) Construct a stem-and-leaf display of the data.
(c) Construct a box plot.

5. Northern Border University
College of engineering
Industrial Engineering Department
Year : 2020-2021,1st
Term
Course : Probabilities and. Statistics
Course No.: 1405 -204
Sheet No. 1
Dr. Yehya Mesalam
Page 5 of 10
5. In a certain company the mean annual vacation period is 15 day. Fourteen employees were
randomly chosen from this company and their vacation days inquired. The following data were
obtained: 6, 12, 11, 12, 10, 7, 12, 14, 16, 18, 11, 12, 16, 17. Select the correct answer
1. The range value is
a- 6 b- 12
c- 14 d- 18
2. The Mean value is
a- 12.429 b- 12.418
c- 12 d- 3.54
3. The variance value is
a- 6 b- 12.418
c- 12.429 d- 3.54
4. The Standard deviation value is
a- 6 b- 12.418
c- 12.429 d- 3.54
5. The C.V value is
a- 0.5 b- 14
c- 0.283 d- 0.354
6. The Mode value is
a- 6 b- 12
c- 14 d- 18
7. The Median value is
a- 6 b- 12
c- 14 d- 18
8. The sample size is
a- 11 b- 12
c- 14 d- 18
9. The Maximum value is
a- 6 b- 12
c- 14 d- 18
10. The minimum value is
a- 6 b- 7
c- 11 d- 12

6. Northern Border University
College of engineering
Industrial Engineering Department
Year : 2020-2021,1st
Term
Course : Probabilities and. Statistics
Course No.: 1405 -204
Sheet No. 1
Dr. Yehya Mesalam
Page 6 of 10
6. The following data represent the viscosity (friction, as in automobile oil) taken from 120
manufacturing batches (ordered from lowest viscosity to highest viscosity).
12.6 12.8 13.0 13.1 13.3 13.3 13.4 13.5 13.6 13.7 13.7 13.7 13.8
13.8 13.9 13.9 14.0 14.0 14.0 14.1 14.1 14.1 14.2 14.2 14.2 14.3
14.3 14.3 14.3 14.3 14.3 14.4 14.4 14.4 14.4 14.4 14.4 14.4 14.4
14.5 14.5 14.5 14.5 14.5 14.5 14.6 14.6 14.6 14.7 14.7 14.8 14.8
14.8 14.8 14.9 14.9 14.9 14.9 14.9 14.9 14.9 15.0 15.0 15.0 15.0
15.1 15.1 15.1 15.1 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.3
15.3 15.3 15.3 15.3 15.4 15.4 15.4 15.4 15.5 15.5 15.6 15.6 15.6
15.6 15.6 15.7 15.7 15.7 15.8 15.8 15.9 15.9 16.0 16.0 16.0 16.0
16.1 16.1 16.1 16.2 16.3 16.4 16.4 16.5 16.5 16.6 16.8 16.9 16.9
17.0 17.6 18.6
Using 7 equal intervals with the lowest starting at 12.
(a) Set up a frequency and a relative frequency distribution.
(b) Construct a frequency polygon and a frequency histogram.
(c) Construct a relative frequency histogram
(d) The median and the mode (analytically and graphically)
(e) The mean and the variance using both the long method and the short-cut method.
(f) Set up a less than and an or-more frequency distributions.
(g) Construct the two O-gives.
(h) Estimate the value below which 75% of the viscosity values fall.
(i) What conclusions can you reach about the viscosity of the chemical?

7. Northern Border University
College of engineering
Industrial Engineering Department
Year : 2020-2021,1st
Term
Course : Probabilities and. Statistics
Course No.: 1405 -204
Sheet No. 1
Dr. Yehya Mesalam
Page 7 of 10
7. Complete the table, then select the correct answer.
Class limit f % f d f *d f *d2
10 - 19 10 10 3
- 30
- 90
20 - 29 10 2
- -20 40
30 - 39 f1=22 1
- f1
- 22
40 - 49 25 25 0 0 0
50 - 59 f2=23 1 f2 23
60 - 69 10 2 20 40
Sum 100 -29 215
1. The lower limit for third interval is
a- 29.5 b- 30
c- 39.5 d- 39
2. The upper limit for third interval is
a- 29.5 b- 30
c- 39.5 d- 39
3. The upper boundary for first interval
is
e- 19.5 f- 20
g- 29.5 h- 29
4. The lower boundary for second interval
is
a- 19.5 b- 20
c- 29.5 d- 29
5. The mean value is
a- 45.5 b- 41.6
c- 42.7 d- 14.445
6. The variance value is
a- 45.5 b- 41.6
c- 208.67 d- 14.445
7. The Standard deviation value is
a- 45.5 b- 41.6
c- 42.7 d- 14.445

8. Northern Border University
College of engineering
Industrial Engineering Department
Year : 2020-2021,1st
Term
Course : Probabilities and. Statistics
Course No.: 1405 -204
Sheet No. 1
Dr. Yehya Mesalam
Page 8 of 10
8. The C.V value is
a- 6 b- 12.418
c- 18 d- 3.54
9. The Mode value is
a- 45.5 b- 41.6
c- 42.7 d- 14.445
10. The Median value is
a- 45.5 b- 41.6
c- 42.7 d- 14.445
11. The total frequency (sample size) is
a- 6 b- 7
c- 10 d- 100
12. The relative frequency for class two is
a- 0.1 b- 10%
c- 10 d- 100
13. The percentage frequency for first class
is
a- 0.1 b- 10%
c- 10 d- 100
14. The percentage frequency for first class
is
a- 0.1 b- 10%
c- 10 d- 100
15. The class width is
a- 6 b- 7
c- 10 d- 100
16. The number of intervals are
a- 6 b- 7
c- 10 d- 100
17. The class mark for fourth class is
e- 40 f- 40.5
g- 44.5 h- 49.5

9. Northern Border University
College of engineering
Industrial Engineering Department
Year : 2020-2021,1st
Term
Course : Probabilities and. Statistics
Course No.: 1405 -204
Sheet No. 1
Dr. Yehya Mesalam
Page 9 of 10
8. Given the following frequency distribution;
Time (min) 11-20 21-30 31-40 41-50 51-60 61-70 71-80 Total
Frequency 3 7 12 16 10 8 4 60
Find (a) Mean and standard deviation by both long and short method;
(b) The coefficient of variation (c) the median; (d) the mode.

10. Northern Border University
College of engineering
Industrial Engineering Department
Year : 2020-2021,1st
Term
Course : Probabilities and. Statistics
Course No.: 1405 -204
Sheet No. 1
Dr. Yehya Mesalam
Page 10 of 10
9. Complete the table then calculates the C.V, mode and median graphically.
Class limit f d f.d f.d2
-
-
-
- 0
-
-
-
0
12
25
45
57
80
86
33
10
0
0
10
20
30
40
50
60
70
80
90
100
31.95 44.95 57.95 70.95 83.95 96.95 109.95122.95