Lecture 03 Part 02 - All Examples of Chapter 02 by Muhammad Haroon
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The document provides examples of statistical analysis, including the construction of frequency distributions and relative frequencies for various datasets involving children in families and patient ages. It demonstrates methods for calculating range, class boundaries, and cumulative frequency distributions, as well as relative frequencies for marks obtained by students. Several examples are presented to illustrate these statistical concepts and calculations.
Lecture 03 Part 02 - All Examples of Chapter 02 by Muhammad Haroon
- 1. Probability & Statistics BSCS Muhammad Haroon-PhD Enrolled (CS) from HITEC University Taxila [email protected] Example 2.1: The following data shows the number of children in different families of a small locality: 1, 2, 4, 3, 0, 1, 2, 3, 1, 1, 0, 2, 1, 0, 2, 3, 0, 0, 1, 3. Make a frequency distribution. Also find relative frequencies. Solution: Range = Maximum Value – Minimum Value = 4 – 0 = 4 The Number of Children Tally The Number of Families (f) Relative Frequency R.F = 𝒇 𝚺𝒇 0 //// 5 5/20 = 0.25 1 //// / 6 6/20 = 0.30 2 //// 4 4/20 = 0.20 3 //// 4 4/20 = 0.20 4 / 1 1/20 = 0.05 𝚺 20 1.00 Example 2.2: The following data shows the ages of 50 cancer patients admitted in Shaukat Khanum Memorial Hospital, Lahore. 48 29 39 32 54 33 44 36 38 31 46 30 20 44 47 39 42 35 33 47 31 35 34 42 41 42 43 35 32 35 43 36 37 45 46 41 25 27 26 40 38 41 44 47 45 45 52 43 44 43 Make a frequency distribution. Also find class boundaries & mid points Solution: The following steps are involved in constructing a frequency distribution. 1) Range = Maximum Value – Minimum Value = 54 – 20 = 34 2) Approximate number of classes Number of classes = 1 + 3.322 log 𝑛 = 1 + 3.322 log(50) = 1 + 3.322 (1.6990) = 6.6066 ≅ 7 (Approximately) 3) With of class interval
- 2. Probability & Statistics BSCS Muhammad Haroon-PhD Enrolled (CS) from HITEC University Taxila [email protected] h = 𝑅𝑎𝑛𝑔𝑒 𝑛𝑜.𝑜𝑓 𝑐𝑙𝑎𝑠𝑠𝑒𝑠 = 34 7 = 4.8571 ≅ 5 (Approximately) 4) Group the entire data with an interval of 5 each and write down the classes in the first column under the heading “Ages”. Count the actual number falling in each interval putting a tally (/) in the proper interval for each value. Count the number of tallies for each interval & write down in the next column, these are frequencies denoted by f. Ages (Class Limits) Tally f Class Boundaries Mid Points 20 - 24 / 1 19.5 – 24.5 22 25 – 29 //// 4 24.5 – 29.5 27 30 - 34 //// /// 8 29.5 – 34.5 32 35 – 39 //// //// / 11 34.5 – 39.5 37 40 - 44 //// //// //// 15 39.5 – 44.5 42 45 - 49 //// //// 9 44.5 – 49.5 47 50 - 54 // 2 49.5 – 54.5 52 𝚺 50 Example 2.3: Make a cumulative frequency distribution. Also find relative frequency & cumulative relative frequency for the following data: Ages f 20 - 24 1 25 – 29 4 30 - 34 8 35 – 39 11 40 - 44 15 45 - 49 9 50 - 54 2 Solution: Ages f Class Boundaries Cumulative frequency (c.f) Relative Frequency R.F = 𝒇 𝚺𝒇 C.R.F = 𝒄.𝒇 𝚺𝒇 20 - 24 1 19.5 – 24.5 1 1/50 = 0.02 0.02 25 – 29 4 24.5 – 29.5 1 + 4 = 5 0.08 0.10 30 - 34 8 29.5 – 34.5 5 + 8 = 13 0.16 0.26 35 – 39 11 34.5 – 39.5 13 + 11 = 24 0.22 0.48 40 - 44 15 39.5 – 44.5 24 + 15 = 39 0.30 0.78 45 - 49 9 44.5 – 49.5 39 + 9 = 48 0.18 0.96 50 - 54 2 49.5 – 54.5 48 + 2 = 50 0.04 1.00 𝚺 50 1.00
- 3. Probability & Statistics BSCS Muhammad Haroon-PhD Enrolled (CS) from HITEC University Taxila [email protected] Example 2.4: Following is the distribution of marks obtained by 50 students in Computer Science. Marks Y > 0 Y > 10 Y > 20 Y > 30 Y > 40 Y > 50 No. of Students 50 46 40 20 10 3 1) Make a frequency distribution of the data 2) Find mid points & make a relative frequency distribution of the data Solution: 1) Marks No. of students (c.f) Classes f Y > 0 50 0 – 10 50 – 46 = 4 Y > 10 46 10 – 20 46 – 40 = 6 Y > 20 40 20 – 30 40 – 20 = 20 Y > 30 20 30 – 40 20 – 10 = 10 Y > 40 10 40 – 50 10 – 3 = 7 Y > 50 3 50 – 60 3 2) Classes Frequency (f) Mid points (Y) Relative Frequency R.F = 𝒇 𝚺𝒇 0 – 10 4 5 4/50 = 0.08 10 – 20 6 15 0.12 20 – 30 20 25 0.40 30 – 40 10 35 0.20 40 – 50 7 45 0.14 50 – 60 3 55 0.06 𝚺 50 1.00 Example 2.5: Find out cumulative relative frequency distribution from the following data Y 6 7 8 9 10 11 12 13 Frequency 24 66 80 48 28 14 4 1 Where Y denoted the member of hours worked in a day workmen in a factory.
- 4. Probability & Statistics BSCS Muhammad Haroon-PhD Enrolled (CS) from HITEC University Taxila [email protected]
- 5. Probability & Statistics BSCS Muhammad Haroon-PhD Enrolled (CS) from HITEC University Taxila [email protected]
- 6. Probability & Statistics BSCS Muhammad Haroon-PhD Enrolled (CS) from HITEC University Taxila [email protected]
- 7. Probability & Statistics BSCS Muhammad Haroon-PhD Enrolled (CS) from HITEC University Taxila [email protected]
- 8. Probability & Statistics BSCS Muhammad Haroon-PhD Enrolled (CS) from HITEC University Taxila [email protected]
- 9. Probability & Statistics BSCS Muhammad Haroon-PhD Enrolled (CS) from HITEC University Taxila [email protected]
- 10. Probability & Statistics BSCS Muhammad Haroon-PhD Enrolled (CS) from HITEC University Taxila [email protected]
- 11. Probability & Statistics BSCS Muhammad Haroon-PhD Enrolled (CS) from HITEC University Taxila [email protected]
- 12. Probability & Statistics BSCS Muhammad Haroon-PhD Enrolled (CS) from HITEC University Taxila [email protected]