---
title: "Preprocessing steps, binning, normalization"
subject: "Data Mining"
chapter: 2
key: "semester_7/data_mining:preprocessing-binning-normalization"
source: https://www.bctengineer.com/q/semester_7/data_mining/preprocessing-binning-normalization
site: BCT Engineering
---

# Preprocessing steps, binning, normalization

Data Mining · Chapter 2: Data Pre-processing

- Asked in: year not given, 2+3+3 marks
- Video: [#8 Data Preprocessing In Data Mining - 4 Steps |DM|](https://www.youtube.com/watch?v=j0tqUBhs-Nc) — Trouble- Free
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/data_mining/preprocessing-binning-normalization
- Whole chapter: https://www.bctengineer.com/md/semester_7/data_mining/chapter-2

## Question

List the steps of data preprocessing. Explain binning method to handle noisy data and normalization techniques for data transformation.

## Short answer

Data preprocessing steps: cleaning, integration, transformation, reduction, discretization. Binning smooths noisy data by sorting, partitioning into equal-frequency or equal-width bins, and replacing values with bin mean, median, or boundary. Normalization scales attributes: min-max to [0,1], z-score using (v-mean)/σ, decimal scaling by dividing by 10^j.

## Answer

#### Steps of data preprocessing
1. Data cleaning
2. Data integration
3. Data transformation
4. Data reduction
5. Data discretisation (and concept hierarchy generation)

#### Binning method for noisy data
Binning smooths sorted data by using its neighbourhood ("local smoothing"). Steps: sort the data, partition into equal-frequency (equal depth) or equal-width bins, then replace each value by the bin mean, median or nearest boundary.

Data: 4, 8, 15, 21, 21, 24, 25, 28, 34 (bins of 3 values)

| Bin | Original | By means | By boundaries |
|---|---|---|---|
| 1 | 4, 8, 15 | 9, 9, 9 | 4, 4, 15 |
| 2 | 21, 21, 24 | 22, 22, 22 | 21, 21, 24 |
| 3 | 25, 28, 34 | 29, 29, 29 | 25, 25, 34 |

#### Normalisation techniques
Normalisation scales attribute values to a small range so that attributes with large ranges do not dominate. Example data: 200, 300, 400, 600, 1000 (min = 200, max = 1000, mean = 500, standard deviation σ = 282.84 using the population formula).

1. **Min-max normalisation** to [0, 1]: v' = (v − min) / (max − min)
   - 200 → 0; 300 → 100/800 = 0.125; 400 → 0.25; 600 → 0.5; 1000 → 1.
2. **Z-score normalisation**: v' = (v − mean) / σ
   - 200 → −1.06; 300 → −0.71; 400 → −0.35; 600 → 0.35; 1000 → 1.77.
3. **Decimal scaling**: v' = v / 10ʲ, with j the smallest integer so max(|v'|) < 1. Here j = 4.
   - 200 → 0.02; 300 → 0.03; 400 → 0.04; 600 → 0.06; 1000 → 0.1.

**Answer:** min-max gives 0, 0.125, 0.25, 0.5, 1; z-score gives −1.06, −0.71, −0.35, 0.35, 1.77; decimal scaling gives 0.02, 0.03, 0.04, 0.06, 0.1.

## Check yourself

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

1. How does smoothing by bin means work?
   A. Replace each value by the overall mean
   B. Sort the data, partition into bins, replace each value by its bin mean
   C. Delete the smallest bin
   D. Scale values to [0,1]
   Answer: B. Binning smooths locally using each sorted bin's mean, median or boundaries. (Key point: Binning steps)

2. For bin (4, 8, 15), what is the smoothing by means?
   A. 4, 4, 15
   B. 8, 8, 8
   C. 9, 9, 9
   D. 15, 15, 15
   Answer: C. (4 + 8 + 15)/3 = 9, so all values become 9. (Key point: Bin mean calculation)

3. Using min-max to [0,1] with min = 200, max = 1000, what is 300 mapped to?
   A. 0.3
   B. 0.1
   C. 0.25
   D. 0.125
   Answer: D. (300 - 200)/(1000 - 200) = 100/800 = 0.125. (Key point: Min-max normalisation)

4. For maximum value 1000, what j is used in decimal scaling and what is 600 mapped to?
   A. j = 4, 0.06
   B. j = 3, 0.6
   C. j = 4, 0.6
   D. j = 3, 0.06
   Answer: A. j is the smallest integer with max|v'| < 1; 1000/10^3 = 1 is not < 1, so j = 4 and 600 becomes 0.06. (Key point: Decimal scaling)

## Related in Data Mining

- [Data preprocessing and handling noisy data](https://www.bctengineer.com/question.md?key=semester_7%2Fdata_mining%3Apreprocessing-noisy-data) — Data Mining, chapter 2
- [Data cleaning: missing, noisy, outliers](https://www.bctengineer.com/question.md?key=semester_7%2Fdata_mining%3Adata-cleaning) — Data Mining, chapter 2
- [Short note: Data preprocessing](https://www.bctengineer.com/question.md?key=semester_7%2Fdata_mining%3Adata-preprocessing-note) — Data Mining, chapter 2
- [Processes in data preprocessing](https://www.bctengineer.com/question.md?key=semester_7%2Fdata_mining%3Apreprocessing-processes) — Data Mining, chapter 2

## Related in other subjects

- [How transformation reduces design steps; band stop design](https://www.bctengineer.com/question.md?key=semester_5%2Ffilter_design%3Abandstop-design-steps-reduction) — Filter Design, chapter 3