🧱 Unit 1 – Data Structures & Algorithms · Lesson 14
Understanding Data & Statistics
What is data?
Data is a collection of raw facts – numbers, text, images, sounds – recorded about something. When data is organised and processed so that it becomes meaningful, it is called information. Schools, banks, hospitals and apps all take decisions based on data.
Structured vs unstructured
Structured data
- Organised in rows and columns
- Fixed format (tables, spreadsheets, databases)
- Easy to search and analyse
- Example: marks sheet, railway reservation
Unstructured data
- No fixed format
- Text, images, audio, video, posts
- Needs special tools to analyse
- Example: emails, photos, YouTube videos
Data life cycle
- 1Collection – gather data from forms, sensors, surveys, websites
- 2Storage – save it in files, databases or the cloud
- 3Processing – clean, sort, calculate, summarise
- 4Analysis & presentation – tables, charts, reports
- 5Decision – use the information
Collection & storage
Data can be collected manually (registers, survey forms) or automatically (barcode scanners, sensors, online forms). It is stored in files (text, CSV), spreadsheets, databases (MySQL) or cloud storage. Storage devices include HDD, SSD and pen drives.
Processing data
Raw data often has blanks, spelling errors or invalid entries. Cleaning removes or fixes them before calculation.
Python
# Processing raw data: clean, then summarise
raw = ['45', ' 67', 'abs', '89 ', '', '72']
clean = []
for v in raw:
v = v.strip()
if v.isdigit():
clean.append(int(v))
print('Valid:', clean, '| ignored:', len(raw) - len(clean))
print('Average:', round(sum(clean) / len(clean), 2))Valid: [45, 67, 89, 72] | ignored: 2
Average: 68.25
Statistical techniques
➗
MeanSum of values ÷ count. The usual “average”.🎯
MedianMiddle value after sorting.🔁
ModeThe value that occurs most often.↔️
RangeMaximum − minimum.📐
Standard deviationHow far values spread from the mean.Statistics in Python
Python
marks = [56, 72, 91, 72, 64, 85, 72, 48, 90, 60]
n = len(marks)
mean = sum(marks) / n
s = sorted(marks)
if n % 2 == 0:
median = (s[n // 2 - 1] + s[n // 2]) / 2
else:
median = s[n // 2]
mode = max(set(marks), key=marks.count)
print('Sorted:', s)
print('Mean :', mean)
print('Median:', median)
print('Mode :', mode)
print('Range :', max(marks) - min(marks))Sorted: [48, 56, 60, 64, 72, 72, 72, 85, 90, 91]
Mean : 71.0
Median: 72.0
Mode : 72
Range : 43
Python
import statistics as st
marks = [56, 72, 91, 72, 64, 85, 72, 48, 90, 60]
print('mean :', st.mean(marks))
print('median :', st.median(marks))
print('mode :', st.mode(marks))
print('pstdev :', round(st.pstdev(marks), 2)) # population SD
print('pvar :', round(st.pvariance(marks), 2))mean : 71
median : 72.0
mode : 72
pstdev : 13.73
pvar : 188.4
Standard deviation
SD = √( Σ(x − mean)² ÷ n ). Steps: find the mean, subtract it from each value, square, average the squares (variance), take the square root.
Python
# Standard deviation by formula, step by step
data = [4, 8, 6, 2]
m = sum(data) / len(data)
sq = [(x - m) ** 2 for x in data]
var = sum(sq) / len(data)
print('mean =', m)
print('squared deviations =', sq)
print('variance =', var, '| SD =', round(var ** 0.5, 3))mean = 5.0
squared deviations = [1.0, 9.0, 1.0, 9.0]
variance = 5.0 | SD = 2.236
Summary
- Data → processing → information.
- Structured data fits tables; unstructured data does not.
- Mean, median, mode, range and SD summarise a data set; Python's
statisticsmodule computes them.
Frequently Asked Questions
What is the difference between data and information?
Data is raw facts (marks of 40 students). Information is processed data that has meaning (class average is 71).
Which measure is not affected by extreme values?
The median, because it depends only on the middle position, not on the size of the largest or smallest values.
What does standard deviation tell us?
How spread out the values are around the mean. A small SD means values are close to the mean.
