Practice Problems: Probability and Statistics
Subject: Probability and Statistics
Practice Problems [No need to submit as a Homework]
Instructor: Prof. M. Hamid
Student Name:
Student ID:
Degree Program:
AI
CST
Question # 01: Calculate the Measures of Central Tendency for the following.
1. Find the mean of the following data set: 2, 5, 8, 12, 15.
2. Find the median of the data set: 5, 9, 12, 16, 20.
3. Find the mode of the data set: 7, 9, 9, 10, 12.
4. Calculate the mean of the numbers: 3, 5, 8, 11, 14, 17.
5. Determine the median of the data set: 1, 2, 4, 5, 8, 9, 10.
6. What is the mode of this data set: 4, 4, 5, 5, 6, 7, 8?
7. For the data set: 2, 4, 6, 8, 10, find the quartiles.
8. Find the first quartile (Q1) of the data set: 3, 5, 7, 8, 10, 13.
9. Find the third quartile (Q3) of the data set: 3, 5, 8, 10, 12, 15.
10. For the data set: 10, 12, 15, 18, 22, 26, 29, find the median.
11. Determine the decile of the data set at 50% position: 10, 14, 17, 18, 20, 25, 30, 35.
12. Find the percentile at 60% for the data set: 2, 6, 8, 12, 14, 16.
13. Compute the mean for the following marks of students: 55, 70, 85, 90, 95.
14. What is the mode for the data set: 4, 5, 6, 7, 7, 8, 9, 9, 9?
15. Calculate the quartiles for the data set: 5, 8, 11, 15, 16, 18, 19, 22, 25.
16. Find the median for the data: 12, 14, 16, 18, 19, 22, 30.
17. Determine the first quartile (Q1) and third quartile (Q3) for data set: 6, 8, 12, 15, 19, 20.
18. Find the mode for the following data set: 5, 5, 6, 7, 8, 9, 10, 10, 10.
19. Calculate the percentile for the 75% position of the data: 4, 6, 8, 12, 14, 18.
20. Calculate the decile for the 40% position in this data: 10, 15, 20, 25, 30, 35, 40, 50.
Question # 02: Compute Measures of Dispersion for the following.
1) Find the range of the data set: 3, 5, 8, 12, 15.
2) Calculate the range for the data: 10, 20, 25, 30, 40.
3) Compute the quartile deviation for the data: 6, 8, 10, 12, 14, 16, 18.
4) Calculate the mean deviation for the data: 7, 9, 10, 12, 14.
5) Find the variance for the data set: 4, 5, 7, 9, 10.
6) Compute the standard deviation for the data: 10, 15, 20, 25, 30.
7) Find the range for the following data: 10, 13, 15, 17, 20.
Not Failure but low aim is a crime.
No defeat is final until you stop trying.
☺ Good Luck ☺
Practice Problems: Probability and Statistics
8) Calculate the variance for the data set: 2, 4, 8, 10, 12.
9) Compute the mean deviation for the data set: 5, 9, 12, 15, 20.
10) Find the standard deviation for the data set: 1, 2, 3, 4, 5.
11) Calculate the variance for the following set of marks: 40, 60, 80, 100, 120.
12) Find the range for the following numbers: 2, 5, 7, 8, 10.
13) Determine the quartile deviation for the data: 6, 8, 10, 12, 14.
14) Calculate the mean deviation of the following data: 11, 14, 16, 19, 20.
15) Compute the standard deviation for the data set: 12, 15, 18, 20, 25.
16) Calculate the variance for the following data: 10, 20, 30, 40, 50.
17) Find the range for the following data: 11, 13, 17, 19, 22.
18) Compute the quartile deviation for the data set: 2, 4, 5, 6, 8, 10, 12.
19) Calculate the standard deviation for the following data: 3, 7, 8, 10, 15.
20) Find the variance for the following data: 25, 35, 45, 55, 65.
Question # 03: The following dataset represents the number of lines of code written by 200
software developers working on various AI projects. The data is provided as individual values of
lines of code written.
50, 80, 120, 130, 140, 150, 180, 200, 220, 230, 240, 250, 270, 300, 350, 400, 420, 450, 480, 500,
55, 75, 110, 120, 145, 170, 190, 210, 230, 250, 270, 310, 340, 380, 400, 430, 460, 490, 510, 530,
60, 85, 125, 135, 145, 155, 180, 210, 230, 250, 280, 310, 350, 370, 400, 430, 460, 490, 510, 540,
70, 90, 130, 140, 150, 160, 180, 190, 220, 240, 260, 300, 330, 360, 390, 420, 450, 480, 510, 550,
65, 95, 115, 125, 135, 155, 175, 200, 220, 250, 280, 310, 330, 360, 380, 410, 440, 470, 500, 530,
50, 80, 110, 120, 140, 160, 170, 190, 210, 230, 240, 270, 300, 330, 350, 370, 400, 420, 440, 460,
60, 90, 120, 130, 150, 160, 180, 210, 220, 240, 260, 290, 320, 340, 360, 380, 410, 440, 470, 500.
▪ Task-I: Construct a frequency distribution table in tabular form for this data. Include the class
intervals and the corresponding frequencies. [Take class width = 50]
▪ Task-II: Based on the frequency distribution constructed in Task 1. Calculate the following
measures of central tendency.
a) Mean of the data.
b) Median of the data.
c) Mode of the data.
d) Quartiles (Q1, Q2, Q3) of the data.
e) Deciles for the data (D2, D4, D7).
f) Percentiles for the data (P40, P60, P80).
▪ Task-III: Based on the frequency distribution constructed in Task 1. Calculate the following
measures of dispersion:
a. Range of the data.
b. Quartile Deviation of the data.
c. Mean Deviation (about mean, median and mode) of the data.
d. Standard Deviation of the data.
e. Variance of the data.
•
Compute the all-related coefficients of (a)-(e) or relative Deviations.
Not Failure but low aim is a crime.
No defeat is final until you stop trying.
☺ Good Luck ☺