Collection, Classification and Presentation of Data: Frequency Distribution, Histogram, Ogive and Pie Chart for SSC Statistics

Every statistical analysis starts with collecting the data and presenting it in a clear form. SSC CGL (Statistics paper) and SSC JSO ask questions on the types of data, the frequency distribution, the class mark, the cumulative frequency and the graphs. This guide on collection, classification and presentation of data for SSC explains all of these with formulas, solved examples and practice questions.

Types of Data

Methods of Collecting Primary Data

• Direct personal investigation (interview).
• Indirect oral investigation (through third persons).
• Questionnaires or schedules sent by mail or filled by enumerators.
• Observation and experiment.
• Telephone and online surveys.

Classification and Tabulation

Classification is the grouping of data into classes. The types are geographical, chronological, qualitative and quantitative (according to numerical value). Tabulation is the arrangement of the classified data in rows and columns. The parts of a table are the title, stub, caption, body, headnote and footnote.

Frequency Distribution

• To convert an inclusive class into an exclusive class, subtract half of the gap (0.5) from the lower limit and add it to the upper limit: 10–19 becomes 9.5–19.5.
• Sturges’ rule for the number of classes: k = 1 + 3.322 log N.
• Cumulative frequency can be “less than” type (adds from the top) or “more than” type (adds from the bottom).

Graphical Presentation

Solved Examples

Example 1. Find the class mark of the class 10–20.
(10 + 20)/2 = 15.

Example 2. Convert the inclusive class 20–29 into an exclusive class.
19.5–29.5.

Example 3. In a pie chart, 30 out of 120 students prefer cricket. What is the angle of the cricket sector?
30/120 × 360 = 90°.

Example 4. The frequencies of four classes are 5, 8, 12 and 5. Find the cumulative frequencies.
5, 13, 25, 30.

Example 5. The less-than and more-than ogives of a distribution intersect at the value 45. What does the point represent?
The median is 45.

Tricks

• Remember that the intersection of the two ogives gives the median.
• The histogram is used to find the mode graphically.
• For a pie chart, always use 360° for the total.
• In inclusive classes, first convert to the true class limits before calculating the mean or median.

Quick Tips

• Learn the difference between primary and secondary data.
• Convert inclusive classes to exclusive classes before calculations.
• Remember that the ogive gives the median.
• Use 360 degrees for pie charts.

Quick Revision Points

• Class mark = (L + U)/2.
• Histogram: continuous data; bar chart: discrete.
• Ogive intersection = median.
• Pie chart angle = value/total × 360.
• Sturges’ rule: k = 1 + 3.322 log N.

Practice Questions With Answers

1. Find the class mark of 40–50.
   Answer: 45
2. What graph is used to find the median graphically?
   Answer: Ogive
3. What graph is used to find the mode graphically?
   Answer: Histogram
4. In a pie chart, 25% corresponds to what angle?
   Answer: 90°
5. Convert the class 30–39 (inclusive) to the exclusive form.
   Answer: 29.5–39.5
6. What is data collected by the investigator first-hand called?
   Answer: Primary data
7. What is the cumulative frequency of the last class equal to?
   Answer: The total frequency
8. What is the class width of 20–30?
   Answer: 10
9. Which data take any value in a range?
   Answer: Continuous data
10. Which diagram joins the mid-points of the tops of the histogram bars?
    Answer: Frequency polygon

How to Practise This Chapter

Practise 10 questions every day and write the steps on paper. Then attempt timed sets from our practice papers and the previous year papers page. See all topics on the Statistics notes page and the next topic Index Numbers.

Frequently Asked Questions

What is primary data?

Data collected first-hand for a specific purpose.

What is secondary data?

Data already collected by someone else and used again.

What is a frequency distribution?

A table showing how often each value or class of values occurs.

What is a class mark?

The mid-value of a class: (lower limit + upper limit)/2.

What is the difference between exclusive and inclusive classes?

In exclusive classes the upper limit is not included in the class; in inclusive classes both limits are included.

What is a histogram?

A graph of a continuous frequency distribution with touching bars.

What is an ogive?

A graph of the cumulative frequency distribution.

How do I find the median from ogives?

It is the x-coordinate of the point where the less-than and more-than ogives meet.

How do I calculate a pie chart angle?

(value/total) × 360°.

What is tabulation?

The systematic presentation of data in rows and columns.

Is this asked in SSC CGL Statistics?

Yes. It forms the base of the descriptive statistics part.

What is Sturges’ rule?

A rule to decide the number of classes: 1 + 3.322 log N.