COMSATS University Islamabad

Sahiwal Campus
(Mechanical Engineering)
Assignment No. 1 (SPRING 2023)

Course Title: Statistics and Probability Theory Course Code: MTH 262 Credit Hours: (3,0)
Course Instructor: Nosheen Ramzan Program Name: BS(ME)
TH
Semester: 4 Batch: 17 Section A Date:
Submission Date: Total Marks: 30
Student’s Name: Reg. No. CUI/ /SWL
CLO1 CLO2 CLO3 CLO4 CLO5
CLOs Max.
Q Nos. Q Nos. Max. Marks. Q Nos. Max. Marks. Q Nos. Max. Marks. Q Nos. Max. Marks.
Addressed Marks.
1 to 20 30
Modules
I and II
Addressed:
Obtained Marks CLO1 CLO2 CLO3 CLO4 CLO5

Marks Secured (Total) Signature of Instructor

Please highlight one Best Sample Average Sample Worst Sample

Note: Use appropriate verb of relevant taxonomy level in all statements.

CLO1-C2-PLO1 (30)
Assignment 1 : Data Presentation: Frequency Distribution Table, Graphical
presentation, measures of central tendency, measures of dispersion

Q.1. The winning scores in the U.S. Masters golf tournament in the years from
1999 to 2008 were as follows:
280, 278, 272, 276, 281, 279, 276, 281, 289, 280
Find the sample mean of these scores.

Q.2. The following is a frequency table giving the ages of members of a symphony
orchestra for young adults.

Find the sample mean of the ages of the 54 members of the symphony.
Q.3. A random sample of 29 students were asked to estimate the average number of
hours they spent per week studying outside of class. Also their eye color and the
number of pets they owned was recorded. The results are given below

Student Gender # Hours # Dress # Pets

s studying Color

1 MALE 10 White 1

2 FEMALE 7 Black 0

3 MALE 15 Brown 3

4 FEMALE 20 Grey 1

5 MALE 40 White 2

6 MALE 25 Blue 1

7 MALE 22 Black 0

8 MALE 13 Blue 5

9 FEMALE 12 White 4

10 MALE 21 Brown 3

11 MALE 16 Black 1

12 MALE 22 White 1

13 FEMALE 25 Blue 1

14 MALE 30 Yellow 2

15 MALE 29 Green 3

16 MALE 25 Brown 5

17 MALE 27 White 4

18 MALE 15 Black 2

19 MALE 14 Black 2

20 FEMALE 17 Brown 1

21 MALE 20 Green 0
 22 MALE 17 Yellow 0

23 MALE 10 Grey 1

24 FEMALE 18 White 2

25 MALE 22 Black 2

26 MALE 15 Black 3

27 FEMALE 14 Grey 0

28 MALE 16 Yellow 0

29 FEMALE 25 Brown 1

a. Construct frequency distribution for # Hours studying.

b. Construct percentage frequency distribution for dress colors of students.
c. Construct relative frequency distribution for # pets of students.
d. Draw histogram for # Hours studying.
e. Draw bar chart for dress colors of students, categorized by male and female.
f. Construct less than cumulative distribution for # hours studying.
g. Draw less than Ogive for # hours studying.
h. Find average # hours studying of students from ungrouped data and also
calculate from frequency distribution of ‘# hours studying.

Q.4. Complete a given table from the following histogram of the number of credit
cards possessed by 80 adults.
 Lower class Upper class frequency Lower Upper Cumulative
boundary boundary class limit class limit frequency

a. Prepare a cumulative frequency distribution.

b. Calculate the cumulative relative frequencies and cumulative percentages for
all classes.
c. Fill in the blanks
i. ______________ number of adults have less than 11.5 credit cards.
ii. ______________ percentage of adults have less than 15.5 credit cards.
iii. ______________ ratio of adults have more than 7.5 credit cards.
iv. ______________ number of adults having credit cards between 4 to
15.
v. _____________ number of adults having less than -0.5 credit cards.
vi. ____________ number of adults having more than 19.5 credit cards.

Q.5. The frequency Ogive of weights (in kg) of 40 persons is given below.

Frequency Ogive

40
37
33

19

34.5 39.5 44.5 49.5 54.5

Complete the table given below

 Lower Upper Cumulative Percentage Lower Upper frequency
class class frequency Cumulative class class
boundary boundary Frequency limit limit

Fill in the blanks

i. __________ number of persons have weight less than 49.5 kg.
ii. ___________ percentage of persons have weight less than 44.5 kg.
iii. ____________ ratio of persons have weight less than 39.5 kg.
iv. ____________ number of persons have weight less than 29.5.

Q.6. The mean of 6, 8, x + 2, 10, 2x - 1, and 2 is 9. Find the value of x and also the
value of the observation in the data.

Q.7. The following observations are arranged in ascending order. The median of
the data is 25 find the value of x.

17, x, 24, x + 7, 35, 36, 46

Q.8. The mean of the following distribution is 2.6. Find the value of p and also the
value of the observation.

xi 0 1 2 3 4 5
fi 3 3 p 7 p-1 4

Q.9. A small company makes and sells cakes. There are 11 employees (including
the owner) in the company whose salaries are given in the table below.
Employe Store Mixer Mixer Baker Baker Head Icer 1 Icer 2 Salesperso Finance Owne
e Perso 1 2 1 2 Baker n Directo r
n r
Salary ($ 15 00 16 50 16 50 17 50 17 50 20 00 18 50 18 50 19 000 75 000 90 00
per Year) 0 0 0 0 0 0 0 0 0

Find the mean, median, and mode for the data of the salaries and determine which the
most appropriate measure of central tendency is.
Q.10. The table shows students’ math test scores.
Scores 0-10 11-21 22-32 33-43 44-54
No. of 3
2 5 30 10
students

i. Work out an estimation for the mean of the scores.

ii. Find median score marks.
iii. Explain the shape of distribution as symmetry or skewed.
iv. In which interval do you think mode will lie?

Q.11. A student's grade in a psychology course is comprised of tests (40%), quizzes

(20%), papers (20%), and a final project (20%). His scores for each of the categories
are 85 (tests), 100 (quizzes), 92 (papers) and 84 (final project). Calculate his overall
grade.

Q.12. 32 is the geometric mean of 16 and what other number?

Q.13. The arithmetic mean and the geometric mean of two positive integers are 10
and 8. Determine the two numbers.

Q.14. The mean of four numbers is 37. The mean of the smallest three of them is 34.
If the range of data is 15 what will be mean for the three largest numbers?

Q.15. Marks of five students are given as 75, 80, 85, 60, and 70. Calculate mean
deviation from mean.

Q.16. A man travels from Jaipur to Agra by a car and takes 4 hours to cover the
whole distance. In the first hour he travels at a speed of 50 km/hr, in the second hour
his speed is 64 km/hr, in third hour his speed is 80 km/hr and in the fourth hour he
travels at the speed of 55 km/hr. find the average speed of the motorist.

Q.17. The population in a city increased at the rate of 15% and 25% for two
successive years. In the next year it decreased at the rate of 5%. Find the average rate
of growth.
Hint: Let us assume that the population is 100

Percentage Population at
rise in the end of
Population year
𝑥𝑖
15 115
25 125
5 95
Q.18. Find the mean of a sample consisting of measurements 1⁄2 , 1⁄4 , 1⁄3 , 1⁄2 ,
𝑎𝑛𝑑 1⁄6 by using coded measurements 6, 3, 4, 6, and 2.

Q.19. Faculty salaries for a random sample of teachers in the public school system of
a certain town were coded by dividing each salary by 1000. Find the average salary of
teachers if the coded values are 18, 15, 21, 19, 13, 15, 14, 23, 18 and 16 dollars.

Q.20. At the end of the cruise, guests pay one bill that covers all on-board
transactions. Suppose that 60 single travellers were surveyed as to their on-board bills
for a seven-day cruise from Los Angeles to the Mexican Riviera. Following is a
summary of the bills.
Amount($) Frequency
51–100 5
101–150 10
151–200 15
201–250 15
251–300 10
301–350 5

i. Find mean value of on-board bills for single travellers

ii. Find median
iii. What do you say about shape of distribution? Symmetrical or skewed. Justify
your answer
iv. Find variance and standard deviation.
v. How many percentage of travellers are within 𝑥̅ ± 1𝑠

Submission date: 16/03/2023