- 2070 Asar · 3+3 marks
Mean and SD of five marks; add 10
Short answer
Mean = 250/5 = 50, SD = √(1002/5) ≈ 14.16. Adding 10 marks increases the mean to 60 but leaves the standard deviation unchanged at 14.16.
In statistics paper five candidates obtain the marks as 33, 38, 48, 59 and 72. Calculate the mean and standard deviation of these marks. If 10 marks are added for each student, what will be mean and standard deviation?
The marks are 33, 38, 48, 59, 72 (n = 5). The five candidates are treated as the whole group, so the SD uses divisor n.
| x | x − x̄ | (x − x̄)² |
|---|---|---|
| 33 | −17 | 289 |
| 38 | −12 | 144 |
| 48 | −2 | 4 |
| 59 | 9 | 81 |
| 72 | 22 | 484 |
| Σ = 250 | 0 | 1002 |
Mean = 250 / 5 = 50
σ² = 1002 / 5 = 200.4
σ = √200.4 = 14.16
(If treated as a sample, s = √(1002/4) = 15.83.)
After adding 10 marks to each candidate
New marks: 43, 48, 58, 69, 82.
New mean = 50 + 10 = 60
Every deviation from the mean stays the same, so the SD does not change: σ = 14.16.
Answer: mean = 50 and SD ≈ 14.16. After adding 10 marks, mean = 60 and SD = 14.16 (unchanged).
✓ Answer checked by Claude Sonnet 5.5
Related questions
- SD of marks; effect of adding one · Probability and Statistics, chapter 1
- Central tendency; mean, median, SD of marks · Probability and Statistics, chapter 1
- Bus ticket counter: mean, SD, CV, CI · Probability and Statistics, chapter 6
- Central tendency and dispersion; median, pass marks · Probability and Statistics, chapter 1
- Ideal central tendency; correct mean and SD · Probability and Statistics, chapter 1
- Corrected mean and SD after item error · Probability and Statistics, chapter 1
- Standard deviation and mean of array · Computer Programming, chapter 7
- Flood statistics and exceedance probability, 2000-2009 · Engineering Hydrology, chapter 6
- HR trickling filter, 2.5 MLD; change if standard · Sanitary Engineering, chapter 7
- Student file displayed in descending marks order · Object Oriented Programming, chapter 8