--- title: "Statistics of 25 days of orders" subject: "Probability and Statistics" chapter: 1 key: "semester_5/probability_and_statistics:new-orders-mean-median-range-sd" source: https://www.bctengineer.com/q/semester_5/probability_and_statistics/new-orders-mean-median-range-sd site: BCT Engineering --- # Statistics of 25 days of orders Probability and Statistics · Chapter 1: Descriptive Statistics and Basic Probability - Asked in: 2068 Jestha (old course), 5 marks - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/probability_and_statistics/new-orders-mean-median-range-sd - Whole chapter: https://www.bctengineer.com/md/semester_5/probability_and_statistics/chapter-1 ## Question The number of new orders received by a company over the first 25 working days were recorded as follows: 3, 0, 1, 4, 4, 4, 2, 5, 3, 6, 4, 5, 1, 4, 2, 3, 0, 2, 0, 5, 4, 2, 3, 3, 5. Determine arithmetic mean, median, range and standard deviation. ## Short answer Mean = 3 orders/day, median = 3, range = 6, sample SD ≈ 1.71 orders/day (n=25, Σx=75, Σx²=295). ## Answer n = 25 values. Ordered data: ```text 0 0 0 1 1 2 2 2 2 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 6 ``` #### Frequency table | x | f | fx | fx² | |---|---|---|---| | 0 | 3 | 0 | 0 | | 1 | 2 | 2 | 2 | | 2 | 4 | 8 | 16 | | 3 | 5 | 15 | 45 | | 4 | 6 | 24 | 96 | | 5 | 4 | 20 | 100 | | 6 | 1 | 6 | 36 | | Total | 25 | 75 | 295 | #### Arithmetic mean ```text x̄ = Σfx / n = 75 / 25 = 3 orders per day ``` #### Median The median is the (n + 1)/2 = 13th value of the ordered data. Counting cumulative frequencies (3, 5, 9, 14, ...), the 13th value is 3. ```text Median = 3 ``` #### Range ```text Range = largest − smallest = 6 − 0 = 6 ``` #### Standard deviation ```text Sxx = Σx² − (Σx)²/n = 295 − 75²/25 = 295 − 225 = 70 s² = 70 / 24 = 2.917 s = √2.917 = 1.708 ``` (With divisor n: σ² = 70/25 = 2.8, σ = 1.673.) **Answer:** mean = 3, median = 3, range = 6, standard deviation ≈ 1.71 orders per day. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the mean number of orders per day? A. 2.5 B. 3 C. 75 D. 4 Answer: B. 75/25 = 3. (Key point: Mean) 2. How is the median located for n = 25? A. The average of 12th and 13th B. The 12th value C. The 13th ordered value, which is 3 D. The 25th value Answer: C. (n+1)/2 = 13th ordered value; cumulative frequencies reach 14 at x = 3. (Key point: Median) 3. What is the range? A. 6 B. 7 C. 5 D. 3 Answer: A. Largest 6 minus smallest 0 = 6. (Key point: Range) 4. What is the sample SD? A. 2.8 B. 1.67 C. 1.71 D. 2.92 Answer: C. Sxx = 295 - 225 = 70, s^2 = 70/24 = 2.917, s = 1.708. (Key point: SD) ## Related in Probability and Statistics - [Central tendency; middle 70% income, median](https://www.bctengineer.com/question.md?key=semester_5%2Fprobability_and_statistics%3Acentral-tendency-middle-70-income) — Probability and Statistics, chapter 1 - [Central tendency; mean, median, SD of marks](https://www.bctengineer.com/question.md?key=semester_5%2Fprobability_and_statistics%3Amean-median-sd-marks-100-students) — Probability and Statistics, chapter 1 - [Breaking strength: average, median, SD](https://www.bctengineer.com/question.md?key=semester_5%2Fprobability_and_statistics%3Abreaking-strength-three-materials) — Probability and Statistics, chapter 1 - [Range and SD of two quiz sections](https://www.bctengineer.com/question.md?key=semester_5%2Fprobability_and_statistics%3Atwo-quiz-sections-range-sd) — Probability and Statistics, chapter 1, asked 2× - [CLT: average resistance of 25 resistors](https://www.bctengineer.com/question.md?key=semester_5%2Fprobability_and_statistics%3Aclt-resistors-mean-below-95) — Probability and Statistics, chapter 4 - [Central tendency and dispersion; median, pass marks](https://www.bctengineer.com/question.md?key=semester_5%2Fprobability_and_statistics%3Acentral-tendency-median-pass-marks) — Probability and Statistics, chapter 1 ## Related in other subjects - [Standard costing variances for a building company](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Avariances-cement-mason-standard-costing) — Engineering Economics, chapter 1 - [Standard deviation and mean of array](https://www.bctengineer.com/question.md?key=semester_1%2Fcomputer_programming%3Astandard-deviation-pseudocode) — Computer Programming, chapter 7 - [EVA; 60 days, 25% work, Rs 12,00,000](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Aeva-numerical-60-days-25-percent) — Project Engineering, chapter 4 - [EVA; 60 days, 25% work, 50% budget spent](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Aeva-numerical-60-days-half-budget) — Project Engineering, chapter 4