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# The range of the data 2, –5, 4, 3, 7, 6 would change if 2 was subtracted from each value in the data. State whether the statement is true or false.

**Solution:**

Given, The __range__ of the data 2, –5, 4, 3, 7, 6 would change if 2 was subtracted from each value in the data.

We have to determine if the given statement is true or false.

We know that the difference between the highest and lowest observations in a given __data__ is called its Range.

Case(i) Arranging the data in __ascending order__, we get

-5, 2, 3, 4, 6, 7

Highest observation = 7

Lowest observation = -5

Range = 7 - (-5)

= 7 + 5

= 12

Case(ii) On subtracting 2 from each value in the data, we get

(2 - 2), (-5 - 2), (4 - 2), (3 - 2), (7 - 2), (6 - 2)

The data becomes 0, -7, 2, 1, 5, 4

Arranging the data in ascending order, we get

-7, 0, 1, 2, 4, 5

Highest observation = 5

Lowest observation = -7

Range = 5 - (-7)

= 5 + 7

= 12

Therefore, the range remains the same in both the cases.

**✦ Try This: **The range of the data 3, –4, 5, 2, 8, 9 would change if 3 was subtracted from each value in the data. State whether the statement is true or false.

**☛ Also Check: **NCERT Solutions for Class 7 Maths Chapter 3

**NCERT Exemplar Class 7 Maths Chapter 3 Problem 48**

## The range of the data 2, –5, 4, 3, 7, 6 would change if 2 was subtracted from each value in the data. State whether the statement is true or false

**Summary:**

The given statement,”The range of the data 2, –5, 4, 3, 7, 6 would change if 2 was subtracted from each value in the data” is false.

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