# Descriptive statistics

> The arithmetic average of numerical observations.

Course: [Practical statistics and inference](https://studybrix.com/en/courses/statistics-foundations/index.md)
Level: university
Prerequisites: High-school algebra.

## Notes

### Mean

The arithmetic average of numerical observations.

### Median

The central ordered value or midpoint of the central pair.

### Standard deviation

A measure of typical spread around the mean.

### Quartile

A cut point dividing ordered data into four broad parts.

## Practice questions

### 1. Which term best matches this description: The arithmetic average of numerical observations.

A. Standard deviation
B. Mean
C. Median
D. Quartile

Answer: Mean

Explanation: Mean is the matching concept in this lesson.

### 2. Which term best matches this description: The central ordered value or midpoint of the central pair.

A. Mean
B. Quartile
C. Median
D. Standard deviation

Answer: Median

Explanation: Median is the matching concept in this lesson.

### 3. Which concept would you apply first in a situation where a measure of typical spread around the mean.

A. Mean
B. Median
C. Quartile
D. Standard deviation

Answer: Standard deviation

Explanation: The scenario directly calls for Standard deviation.

### 4. Name the concept described as: A cut point dividing ordered data into four broad parts.

Answer: Quartile

Explanation: The intended concept is Quartile.

### 5. Which statement about Mean is most accurate?

A. The central ordered value or midpoint of the central pair.
B. A measure of typical spread around the mean.
C. The arithmetic average of numerical observations.
D. A cut point dividing ordered data into four broad parts.

Answer: The arithmetic average of numerical observations.

Explanation: The definition in the lesson notes gives the required condition.

### 6. Explain one important difference between Mean and Median.

Sample answer / marking guidance: Mean: The arithmetic average of numerical observations. Median: The central ordered value or midpoint of the central pair.

Explanation: Credit a clear distinction using both definitions and an appropriate example if supplied.

### 7. Give a short example showing how Standard deviation would be used in practice.

Sample answer / marking guidance: A valid example should demonstrate this idea: A measure of typical spread around the mean.

Explanation: Credit a relevant scenario that applies the concept rather than merely naming it.

### 8. Summarize why Quartile matters in the lesson “Descriptive statistics”.

Sample answer / marking guidance: Quartile matters because A cut point dividing ordered data into four broad parts.

Explanation: Credit the core purpose, scope and any important limitation from the notes.

## Further reading

- https://www.openintro.org/book/os/

Original AI-assisted educational draft; not independently teacher-reviewed. References support further study, not copied exercises, affiliation or curriculum accreditation.