Convert the following frequency distribution into exclusive class intervals.
| Class | f |
|---|---|
| 0 - 7 | 15 |
| 8 - 14 | 15 |
| 15 - 21 | 14 |
| 21 - 28 | 11 |
| 29 - 35 | 5 |
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🔒 Start your 14-day free trial to unlock the full solution →Concept understanding — Frequency Distribution
Frequency Distribution: From Everyday Chaos to Economic Order
Imagine you walk into a bustling market in your city. You see hundreds of people — some buying vegetables, some selling clothes, some just passing through. If someone asked you, "What kind of crowd is here?", you wouldn't list every single person's age, income, or purpose. That would be useless noise.
Instead, you'd naturally group them: "Most people seem to be in their 20s and 30s, a fair number of older folks, and very few children." You've just created a frequency distribution in your head — you've taken raw, chaotic data and organised it into meaningful groups.
The Precise Meaning
A frequency distribution is a table (or graph) that shows how often each distinct value or group of values occurs in a dataset. It answers the question: "How many observations fall into each category?"
In Economics, this is how we make sense of raw data — whether it's household incomes, prices of goods, or exam scores of students.
For a set of data, if x1,x2,…,xn are the values (or class midpoints) and f1,f2,…,fn are their corresponding frequencies, then:
Total number of observations=∑i=1nfi
where ∑ means "sum of", fi is the frequency of the i-th class, and n is the number of classes.
The Two Types You Must Know
1. Individual (Ungrouped) Frequency Distribution — When data has few distinct values. For example, the number of siblings of 20 students: 0, 1, 1, 2, 0, 1, 3, 2, 1, 0, 1, 1, 2, 0, 1, 2, 1, 0, 1, 1. You'd make a table:
| Number of Siblings | Tally Marks | Frequency |
|---|---|---|
| 0 | ||
| 1 | ||
| 2 | ||
| 3 |
2. Grouped Frequency Distribution — When data has many different values, you group them into class intervals. This is what you'll use most in Economics. For example, monthly incomes of 50 households in a village:
| Income (₹) | Number of Households (Frequency) |
|---|---|
| 0 – 5,000 | 8 |
| 5,000 – 10,000 | 15 |
| 10,000 – 15,000 | 12 |
| 15,000 – 20,000 | 10 |
| 20,000 – 25,000 | 5 |
Here, "0 – 5,000" is a class interval, and "8" is its frequency.
Why This Matters in Economics
Economics is about patterns in human behaviour — spending, saving, earning, producing. You cannot see patterns in a jumble of numbers. A frequency distribution reveals them.
Example: Understanding Poverty
Suppose you have income data for 1,000 families. Raw data tells you nothing. But a frequency distribution with class intervals like ₹0–₹5,000, ₹5,000–₹10,000, etc., immediately shows you how many families fall below the poverty line. This single table can guide government policy on subsidies, tax rates, and welfare schemes.
Example: Analysing Market Demand
A shopkeeper records daily sales of a product for 30 days. A frequency distribution of sales volumes tells her which price range or quantity sells most often — directly informing her inventory decisions.
A frequency distribution is not just a table. It is the first step toward every statistical tool you will learn: mean, median, mode, standard deviation, and even regression. Without it, you are trying to read a book with all the letters scrambled.
Key Terms You Must Master …
Adjustment factor = (lower limit of next class − upper limit of previous class)/2 = (8 − 7)/2 = 0.5. Subtract 0.5 from each lower limit and add 0.5 to each upper limit to get continuous (exclusive) classes; frequencies stay unchanged. …
Adjustment factor = (lower limit of next class − upper limit of previous class)/2 = (8 − 7)/2 = 0.5. Subtract 0.5 from each lower limit and add 0.5 to each upper limit to get continuous (exclusive) classes; frequencies stay unchanged.
…
- CBSE 2025Set ANNUAL1 markQ.Fill in the blank: Frequency distribution is a common way of classifying ________ data into a quantitative variable.
›Reveal solutionSolution
A frequency distribution classifies raw data of a quantitative variable.
A frequency distribution is a table that classifies the raw (unorganised) data of a quantitative variable into classes/groups and shows the number of items (frequency) in each class. It is a common way of organising a large mass of raw numerical dat …
- CBSE 2022Set MARCH1 markMCQQ.Upper limit of the class 30-40 is(a) 30(b) 40(c) 35(d) 70
›Reveal solutionSolution
The upper limit of the class 30-40 is 40 — the higher of the two class boundaries.
A class interval has two limits. The lower value written first is the lower limit and the higher value written second is the upper limit. For the class 30-40, therefore, 30 is the lower limit and 40 is the upper limit. The mid-point would be (30+40)/2 = 35 and the width (class size) would be 40-30 = 10, but t …
- CBSE 2020Set ANNUAL1 markMCQQ.The class interval of 25-27 is-(a) 2(b) 4(c) 6(d) 8
›Reveal solutionSolution
The class interval of 25–27 is 2 — option (a).
The class interval (size of a class) is the difference between its upper and lower class limits. For the class 25–27: class …
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