Data Classification and Presentation

Dr. Bhupender Kumar Som
Jun 2, 2022
9 min read

Updated: Aug 12

Drawing conclusion from raw data is very difficult technically, which is also called ungrouped data. Through statistics the data can be grouped in many meaningful ways. Data presentation in frequency distribution is known as grouped data.

Once the data is grouped, it becomes easier to pick out the patterns and to draw the logical conclusion out of it.

In simple words frequency distribution is a tabular summary, grouping the frequencies of observations in each of the several non – overlapping classes.

Classification is a process of arranging the data according to some common characteristic possessed by the facts constituting the data. The facts having a common characteristic are termed as one class or group. Thus classification is the grouping of the related facts into different classes.

Purpose of Classification

To condense the mass of data in such a manner that similarities and dissimilarities are readily apprehended and relationship studied.
To facilitate comparison.
To have a bird’s eye view of the significant features of the data.
To enlighten the important information while giving less prominence to insignificant items.
To utilize the data for tabulation and further statistical analysis.
To eliminate unnecessary details contained in raw data.
To present the complex, scattered data in a concise, logical and understandable form.

Essentials of Good Classification

Classification is done in such a way so that entire data is covered and not even a single item is left unclassified.
Item of the data should belong only to one class by avoiding overlapping.
It should facilitate comparison
Class interval should be of equal length.
Should confirm to the objects of investigation.
It should be flexible.
Items constituting in a group should be homogeneous

Kinds of Classification

Quantitative Classification

If the data is classified on the basis of some quantitative information the classification is known as quantitative

Example

Chronological Classification

When the data is classified on the basis of time it is known as chronological classification. The data is also known as time series data.

Example

Geographical Classification

When data is classified on the basis of geographical information, it is known as geographical classification.

Example

Qualitative Classification

If the data are classified on the basis of some attributes or quality (descriptive characteristics) such as sex, literacy, beauty, honesty, intelligence, religion, education, colour of hair etc. The classification is called qualitative classification. “In this type of classification, the attribute under study cannot be measured but its presence or absence can be found or felt”. This type of classification is called Simple or Dichotomous or Two-fold classification.

Two Fold Classification

Data Presentation

The data can be presented in one of the three ways

Textual Presentation
When the data is presented in text format.
Textual presentation is appropriate when data can be communicated effectively through words, sentences, and a few numerical figures, without requiring a table or graph. It should preferably be used under the following conditions:
- Small volume of data: When only a few observations or figures need to be reported.
- Simple message: When the objective is to communicate one or two key findings rather than detailed comparisons.
- Emphasis on key statistics: When management needs to focus on important figures such as growth rate, market share, or profit change.
- Data accompanied by explanation: When numerical information requires context, reasons, or interpretation.
- Executive summaries and reports: When presenting the major findings of an analysis to senior management.
- No complex comparison is required: When readers do not need to compare many categories or periods simultaneously.
For Example: Instead or providing a report full of tables, charts and figures. The manager may present the report in textual format. That is by quoting a statement, "The Company's revenue increseard from Rs 120 crore in 2025 to Rs. 138 crore in 2026, representing a growth of 15%, primarily driven by stronger marketing campaign and longitivity of festivial season in North"
Tabulation
Tabulation should be used when data need to be systematically arranged in rows and columns to facilitate comparison, analysis, and interpretation.
It is particularly suitable under the following conditions:
- Large volume of data: When textual presentation becomes lengthy or difficult to understand.
- Comparison is required: When values across products, regions, departments, periods, or other categories need to be compared.
- Exact numerical values are important: Unlike graphs, tables allow the reader to see precise figures.
- Data require classification: When information needs to be grouped according to categories or characteristics.
- Multiple variables are involved: For example, comparing sales simultaneously by region and product category.
- Further statistical analysis is required: Tables provide an organized base for calculating averages, percentages, dispersion, correlations, etc.
- Detailed managerial reporting: Useful in MIS reports, financial statements, sales reports, HR reports, and operational reviews.

For Example

Suppose management wants to compare quarterly sales across four regions:

Region	Q1 (₹ Cr.)	Q2 (₹ Cr.)	Q3 (₹ Cr.)	Q4 (₹ Cr.)
North	25	28	31	35
South	30	32	34	38
East	18	21	23	25
West	32	35	39	42

A textual paragraph would make these 16 figures difficult to compare. A table allows management to compare regions as well as quarters simultaneously.

Following are some tabulation distribution esstentials

Frequency Distribution

A frequency distribution is any device such as a graph or table that displays the values that the variable can assume along with the frequency of occurrence of these values either individually or as they are grouped into a set of mutually exclusive and exhaustive intervals

“Frequency distribution is a method of organizing the raw and unorganized data”

Following are the three steps by which the data can be organized:

Step 1: To find the range of given data

Step 2: To get the number of class – intervals

Step 3: To determine the width of the class

Class Intervals

Class intervals are contiguous non-overlapping intervals selected in such a way that they are mutually exclusive and exhaustive

Formation of Frequency Table

The number of times a value occurs in a series is called the frequency of that value and the arrangement obtained by mentioning the frequency against each value in the series is called frequency distribution.

The frequency distributions can be divided into two categories:

a. Discrete Frequency Distribution

b. Continuous Frequency Distribution

Discrete Frequency Distribution

In this distribution the variable under study is listed as discrete number and the frequencies are marked against the particular value depending on times of occurrence.

Table 1.0 - Discrete Frequency Distribution

(Number of cars sold)

Grouped or Continuous Frequency Distribution

In this, the various items of a series are classified into groups or classes. The lowest and highest values that can be included in a class or group are called class limits. The lowest value is known as lower limit and the highest value is known as the upper limit.
The width of the class is known as class interval, the number of items falling within the range of the class interval is called the frequency of that class.

Open and Closed Ended Classes

An open end or undetermined class is a class in which either the lower limit or the upper limit is missing. In general it is applied to more than or less than type classification.
However in practice they are generally avoided because open end classes make it difficult to calculate certain statistical measure like arithmetic mean.

For Example:

Exclusive and Inclusive Classes

In exclusive classes the upper limit of the class is excluded from the particular class and in Inclusive class distribution the upper limit of the classes is included in the particular class.

Example: Exclusive Class Interval

Example: Inclusive Class Interval

As far as possible the inclusive class intervals shall be avoided as it becomes very difficult for respondents to understand at times. Every Inclusive type can be converted in to exclusive type as;

Find the difference between the upper limit of any class and the lower limit of the next class.
Divide the difference found in step 1 by 2.
Subtract the fraction obtained in step 2 from the lower limit of all the classes and add the same fraction to the upper limit of all the classes.

Converting Inclusive Interval in Exclusive

In the previous example the difference between the upper limit of the first class and the lower limit of the second class is 10 – 9 =1. Half of this difference is ½ = 0.5. Hence the previous data can be modified as;

Determination of Number of Classes

Sturge’s has given a formula to determine the number of classes:

Where; K represents the number of classes and N as number of observations.

Determination of Magnitude of Class Intervals

The magnitude of the class interval is given by;

Where; Range=Maximum Value -Minimum Value

Charts and Graphs

Pie Chart

Pie chart is used to show the proportion. A Pie chart shall contain data in percentage only. A complete pie chart represents 100% of the data. More effective for 2 to 4 category proportions

A pie chart should be used when the objective is to show the relative contribution of different categories to a single whole.

It is most appropriate under these conditions:

Part-to-whole relationship: Categories together represent a meaningful total, usually 100%.
Small number of categories: Ideally around 3–6 categories; too many slices make interpretation difficult.
Proportions are more important than exact values: The manager wants to understand relative shares rather than precise numerical differences.
One point in time: It is best for showing composition at a particular period, rather than changes over time.
Categories are mutually exclusive: Each observation should belong to only one category.
Quick visual communication is required: Particularly useful in presentations, dashboards, and executive summaries.

Bar Chart

A bar chart should be used primarily when the objective is to compare the magnitude, frequency, or value of different categories.

It is most appropriate when:

Comparing categories: Such as sales across products, branches, regions, or departments.
Categories are discrete and independent: For example, Marketing, Finance, HR, and Operations.
Differences in magnitude are important: The length of each bar makes comparison easy.
Ranking is required: Useful for identifying the highest/lowest performing products, employees, branches, etc.
Exact comparison is more important than composition: A bar chart is usually better than a pie chart when categories have similar values.
Multiple groups need comparison: Grouped bars can compare, for example, sales of Product A and Product B across regions.

Bar Charts can be horizontal Bars or Verticle Bars

Horizontal Bar Chart Example

Verticle Bar Chart Example

Frequency Polygon (Line Chart)

A line chart or frequency polygon should primarily be used when we want to show how a variable changes over time or across another naturally ordered sequence.

It is most appropriate when:

Time is an important dimension: Data are recorded daily, monthly, quarterly, or annually.
Trend needs to be identified: To determine whether sales, profit, demand, costs, etc. are increasing, decreasing, or stable.
Changes between consecutive periods matter: The connected points make the direction and magnitude of movement visible.
Multiple trends need comparison: For example, comparing sales trends of two products over the same period.
Patterns or fluctuations need detection: Useful for identifying peaks, declines, seasonality, or unusual movements.
Forecasting is required: Historical trends displayed through line charts often form the starting point for business forecasting.

Figure -1

(IDBI Bank Stock Price Movement on 09.07.2019)

Doughnut Chart

A doughnut chart (donut chart) is a variation of a pie chart in which data are displayed as segments of a ring. Each segment represents the proportion or percentage of a category in relation to the whole.

The centre is left blank and can be used to display an important figure such as total sales, total customers, or overall percentage.

Use a doughnut chart when:

Part-to-whole relationship needs to be shown.
Categories together represent 100% or a meaningful total.
There are a small number of categories, preferably around 3–6.
Relative proportions are more important than precise numerical comparison.
A visually attractive presentation is required for a dashboard or management presentation.
You want to display an important KPI or total in the centre of the chart.

For Example

Suppose a retailer's annual revenue of ₹100 crore comes from:

A doughnut chart can immediately communicate the revenue composition, while the centre can display Total Revenue: ₹100 Cr.

Product Category	Revenue Share
Electronics	40%
Fashion	30%
Grocery	20%
Others	10%

key interpretation is:

Electronics is the largest contributor at 40%, followed by Fashion at 30%. Together, these two categories generate 70% of total revenue.

Histogram

A histogram is a graphical method used to show the frequency distribution of continuous quantitative data. It groups numerical observations into class intervals (bins) and represents their frequencies using adjoining bars.

Unlike a bar chart, the bars in a histogram touch each other, indicating the continuous nature of the data.

Histogram can be used when

The variable is quantitative and continuous, such as income, age, weight, delivery time, sales value, or processing time.
There are many observations that need to be summarized.
Data can be grouped into class intervals.
We want to understand the shape of the distribution.
We want to identify concentration, spread, skewness, peaks, or unusual observations.
Management wants to understand where most observations are concentrated, rather than simply compare categories

For Example

Suppose an e-commerce company studies the delivery time of 1,000 orders. Instead of examining 1,000 individual values, the analyst groups them as per the table

Delivery Time	Number of Orders
0–1 days	80
1–2 days	220
2–3 days	350
3–4 days	230
4–5 days	90
5–6 days	30

Pareto Chart

A Pareto chart should be used when the objective is to identify and prioritize the few categories or causes responsible for the largest proportion of a problem or outcome.

It combines:

Bars arranged from highest to lowest frequency/impact.
A cumulative percentage line.

It is closely associated with the Pareto principle (80/20 rule): a relatively small number of causes often account for a large proportion of the effect.

Use a Pareto Chart When:

Problems need prioritization: Management wants to know which issues should be addressed first.
There are multiple causes of a problem: Such as different reasons for customer complaints.
Frequency or impact can be measured: Categories can be ranked by number, cost, loss, defects, complaints, etc.
Resources are limited: Management cannot address every issue simultaneously and needs to identify the "vital few."
Root-cause improvement is required: Particularly useful in quality management, operations, customer service, and process improvement.
Cumulative contribution matters: Management wants to know which combination of causes accounts for, say, 70–80% of the problem.