Q.100 rupee to 200 rupee is the same interval as 700 rupee to 800 rupee. Locations in Cartesian coordinate system is another perfect example of interval scale measurement. Explain why these are examples of interval scale measurement.

Interval Scale Measurement: From Intuition to Precision

Imagine you have a thermometer. It reads 30°C today and 20°C yesterday. You can say two things with confidence: first, today is warmer (the order matters), and second, the difference between today and yesterday is exactly 10°C. That difference is meaningful — 10°C is a real, measurable gap in heat energy.

But can you say that 40°C is "twice as hot" as 20°C? No. Because the zero on a Celsius scale is arbitrary — it was set at the freezing point of water, not at the absence of heat. If you convert to Fahrenheit, 40°C is 104°F and 20°C is 68°F, and 104 is not twice 68. The ratio changes because the zero point moved.

This is the core intuition behind an interval scale: you can compare differences (intervals) between values, but you cannot meaningfully compare ratios. The scale has equal intervals — the gap between 10°C and 20°C is the same size as the gap between 30°C and 40°C — but the zero is arbitrary.

---

The Precise Statement

An interval scale is a measurement scale that satisfies three properties:

1. Order: Values can be ranked (e.g., 30°C > 20°C).
2. Equal intervals: The difference between any two adjacent scale units is constant throughout the scale. A change of 1 unit means the same thing regardless of where you are on the scale.
3. Arbitrary zero: The zero point is not a true zero — it does not mean "none of the quantity being measured." It is a reference point chosen for convenience.

Because of the arbitrary zero, you can add and subtract values (differences are meaningful), but you cannot multiply or divide them (ratios are not meaningful).

---

Key Examples

---

How It Differs from Other Scales

• Nominal scale: Only names categories (e.g., red, blue). No order, no arithmetic. …