Statistical Description of Data for CA Foundation
Statistical description of data: collection, classification, frequency distributions, tabulation, and diagrams and graphs.
Quantitative AptitudePaper 3, Statistics11 MCQs2 lessons2 flashcards3 memory tricks
Practise Statistical Description of Data free
What you'll learn
- Collection and classification
Distinguish types of data and build frequency distributions. - Diagrams and graphs
Choose and read the right diagram.
Key formulas
| Class width | Upper limit − lower limit |
|---|---|
| Mid-value | (Lower + upper) ÷ 2 |
| Class boundaries (inclusive classes) | Limits ± half the gap |
| Frequency density | Frequency ÷ class width |
Concepts explained
Collection and classification of data
Data can be primary (collected first-hand) or secondary (already collected), and is classified by time, place, attribute or value.
What it means
- Primary: surveys, interviews, observation.
- Secondary: published reports, census, RBI data.
- Classification: chronological, geographical, qualitative, quantitative.
- Tabulation arranges classified data in rows and columns.
- A student surveys classmates' study hours
Answer: Primary data
- Rainfall by state
Answer: Geographical classification
Related terms
- Questionnaire: list of questions for respondents
- Sampling: studying part of the population
Exam tip: Who collected it? You → primary; someone else → secondary.
Frequency distributions
A frequency distribution groups data into classes with their frequencies; know limits, boundaries, width and mid-values.
What it means
- Width = upper − lower limit.
- Mid-value = (lower + upper) ÷ 2.
- Inclusive classes → boundaries = limits ± half the gap.
- Exclusive classes include the lower limit and exclude the upper.
- 10–20
Answer: 15
- 10–19 (gap 1)
Answer: 9.5–19.5
Related terms
- Cumulative frequency: running total of frequencies
- Frequency density: frequency ÷ width for unequal classes
Exam tip: Convert inclusive classes to boundaries before drawing a histogram.
Diagrams and graphs
Histograms and frequency polygons show distributions; ogives show cumulative frequencies; pie and bar charts compare parts and categories.
What it means
- Histogram: adjacent rectangles; mode from the tallest bar.
- Ogive: cumulative frequency curve; median where the two ogives meet.
- Pie chart: angle = % × 3.6°.
- Bar diagram: separate bars for categories.
- 25% share
Answer: 90°
- Less-than and more-than ogives cross at 42
Answer: Median = 42
Related terms
- Frequency polygon: line joining mid-points of bar tops
- Time series graph: values over time
Exam tip: Mode → histogram; median → ogive.
Memory tricks
Mode from histogram; median from ogives.
Sector angle = percentage × 3.6°.
Exclusive classes include the lower limit and exclude the upper.
Try 3 CA Foundation-style questions
Q1. For inclusive classes 10–19, 20–29, …, the class boundaries of the first class are
- 10 – 19
- 10 – 20
- 9 – 20
- 9.5 – 19.5
Show answer
Answer: (4) 9.5 – 19.5
Gap between classes is 1, so subtract and add 0.5: 10 − 0.5 = 9.5 and 19 + 0.5 = 19.5.
Q2. Classifying data by states or cities is called
- chronological classification
- qualitative classification
- geographical classification
- quantitative classification
Show answer
Answer: (3) geographical classification
Geographical (spatial) classification groups data by place; chronological by time; qualitative by attribute; quantitative by measured value.
Q3. An ogive is a graph of
- cumulative frequencies
- simple frequencies as bars
- a pie chart
- time series values
Show answer
Answer: (1) cumulative frequencies
An ogive plots cumulative frequency against class boundaries ('less than' or 'more than').
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