---
title: "Range and SD of two quiz sections"
subject: "Probability and Statistics"
chapter: 1
key: "semester_5/probability_and_statistics:two-quiz-sections-range-sd"
source: https://www.bctengineer.com/q/semester_5/probability_and_statistics/two-quiz-sections-range-sd
site: BCT Engineering
---

# Range and SD of two quiz sections

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

- Asked in: 2071 Chaitra, 6 marks; 2068 Jestha (old course), 6 marks (asked 2 times)
- Video: [Measures of Variability (Range, Standard Deviation, Variance)](https://www.youtube.com/watch?v=s7WTQ0H0Acc) — Daniel Storage
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/probability_and_statistics/two-quiz-sections-range-sd
- Whole chapter: https://www.bctengineer.com/md/semester_5/probability_and_statistics/chapter-1

## Question

Two different sections of a statistics class take the same quiz and the scores are recorded below:
Section 1: 1 20 20 20 20 20 20 20 20 20 20
Section 2: 2 3 4 5 6 14 15 16 17 18 19
a) Find the range and standard deviation for each section.
b) What do the range values lead you to conclude about the variation in the two sections?
c) Why is the range misleading in this case?
d) What do the standard deviation values lead you to conclude about the variation in two sections?

## Short answer

Section 1: range 19, SD 5.73. Section 2: range 17, SD 6.74. Range suggests Section 1 varies more, but it is misleading because one outlier (1) inflates range while most scores are identical. SD shows Section 2 actually varies more, giving the correct picture.

## Answer

Range = largest − smallest. The standard deviation uses every value: s = √[Σ(x − x̄)² / (n − 1)]. Both sections have n = 11 students.

#### a) Range and standard deviation

| | Section 1 | Section 2 |
|---|---|---|
| Largest, smallest | 20, 1 | 19, 2 |
| Range | 19 | 17 |
| Σx | 201 | 119 |
| Mean | 18.27 | 10.82 |
| Σ(x − x̄)² | 328.18 | 453.64 |
| s² (÷ 10) | 32.82 | 45.36 |
| s | 5.73 | 6.74 |

(With divisor n the SDs are 5.46 and 6.42; the comparison is the same.)

#### b) Conclusion from the range
The range of Section 1 (19) is larger than that of Section 2 (17), so by range alone Section 1 seems to vary more.

#### c) Why the range is misleading
The range depends only on the two extreme scores. In Section 1, ten students scored exactly 20 and only one student scored 1. That single odd score makes the range large although almost all students are identical. Section 2 has scores spread over the whole scale (2 to 19).

#### d) Conclusion from the standard deviation
The standard deviation (6.74 against 5.73) shows that **Section 2 varies more**, because every score contributes to it. This is the correct picture: Section 1 is concentrated at 20 apart from one outlier, while Section 2 is truly spread out.

**Answer:** Range: 19 and 17. SD: 5.73 and 6.74. Standard deviation is the better measure here.

## Check yourself

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

1. What are the ranges of Section 1 and Section 2?
   A. 19 and 17
   B. 17 and 19
   C. 20 and 19
   D. 1 and 2
   Answer: A. Section 1: 20 - 1 = 19; Section 2: 19 - 2 = 17. (Key point: Range of each section)

2. Why is the range misleading here?
   A. It ignores the units
   B. It depends only on the two extremes, and one odd score (1) inflates it
   C. It uses every score
   D. It is always smaller than SD
   Answer: B. Ten students scored 20, so the single score of 1 makes the range large. (Key point: Why range misleads)

3. What does the standard deviation conclude?
   A. Section 1 varies more
   B. Both vary equally
   C. Section 2 varies more (6.74 vs 5.73)
   D. No conclusion is possible
   Answer: C. SD uses every score, and Section 2's scores are truly spread. (Key point: Conclusion from SD)

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