Q.(OR) Draw Histogram with the help of the following data : Marks 0-10, 10-20, 20-30, 30-40, 40-50; No. of Students 20, 25, 40, 35, 25.

Histogram Bin Width – A First Look

Imagine you're a Class 12 Economics student collecting data on the monthly pocket money of 50 students in your school. You have numbers like ₹200, ₹350, ₹500, ₹1200, and so on. If you just list them, you see nothing. But if you group them — say, ₹0–₹200, ₹200–₹400, ₹400–₹600 — you start to see a pattern: most students get between ₹200 and ₹600, a few get more.

That grouping interval — ₹200 in this example — is the bin width. In a histogram, the horizontal axis is divided into equal-sized bins (intervals), and the height of each bar shows how many observations fall into that bin. The bin width is simply the length of each interval.

The Precise Meaning

For a continuous variable (like income, price, age, or exam score), a histogram is a bar chart where:

• The width of each bar equals the bin width (say, $h$).
• The height of each bar is the frequency (count) of data points in that bin.
• The area of each bar is proportional to the relative frequency.

If you choose a bin width of ₹200, your bins might be:

₹0–₹200, ₹200–₹400, ₹400–₹600, ₹600–₹800, ₹800–₹1000, ₹1000–₹1200.

Why Bin Width Matters

The bin width is not a fixed number — you choose it. And that choice changes the story the histogram tells.

• Too wide (say ₹500): you might get only 2–3 bars. You lose detail — you can't see whether most students get ₹200–₹400 or ₹400–₹600.
• Too narrow (say ₹10): you get many bars, each with very few students. The histogram looks jagged and noisy — you can't see the overall pattern.
• Just right (say ₹200): you see the shape clearly — a peak around ₹300–₹500, a tail towards higher values.

The Formula (Where It Exists)

In Economics, the histogram itself is a graphical tool — it doesn't have a single formula like the multiplier. But the bin width is defined as:

where:

• Range = Maximum value – Minimum value
• Number of bins = chosen by the researcher (often using Sturges' rule or trial and error) …