---
title: "Mean and SD of five marks; add 10"
subject: "Probability and Statistics"
chapter: 1
key: "semester_5/probability_and_statistics:mean-sd-five-candidates-add-ten"
source: https://www.bctengineer.com/q/semester_5/probability_and_statistics/mean-sd-five-candidates-add-ten
site: BCT Engineering
---

# Mean and SD of five marks; add 10

Probability and Statistics · Chapter 1: Descriptive Statistics and Basic Probability

- Asked in: 2070 Asar, 3+3 marks
- Video: [How To Calculate The Standard Deviation](https://www.youtube.com/watch?v=IaTFpp-uzp0) — The Organic Chemistry Tutor
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/probability_and_statistics/mean-sd-five-candidates-add-ten
- Whole chapter: https://www.bctengineer.com/md/semester_5/probability_and_statistics/chapter-1

## Question

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?

## 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.

## Answer

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 |

```text
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.

```text
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).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is the mean of 33, 38, 48, 59, 72?
   A. 52
   B. 48
   C. 250
   D. 50
   Answer: D. 250/5 = 50. (Key point: Mean)

2. Treating the five candidates as the whole group, what is the SD?
   A. 10.02
   B. 15.83
   C. 200.4
   D. 14.16
   Answer: D. Variance = 1002/5 = 200.4, so SD = sqrt(200.4) = 14.16. (Key point: SD divisor)

3. After 10 marks are added to each, what happens?
   A. Mean 60 and SD 24.16
   B. Mean 60 and SD unchanged
   C. Mean 60 and SD 10 times larger
   D. Mean 50 and SD 14.16
   Answer: B. The mean shifts by 10 but deviations from the mean are unchanged, so SD stays 14.16. (Key point: Adding 10)

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