The range of the data 3, 7, 1, –2, 2, 6, –3, –5 would change if 8 was added to each value in the data. State whether the statement is true or false.
Solution:
Given, The range of the data 3, 7, 1, –2, 2, 6, –3, –5 would change if 8 was added to 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, -3, -2, 1, 2, 3, 6, 7
Highest observation = 7
Lowest observation = -5
Range = 7 - (-5)
= 7 + 5
= 12
Case(ii) On subtracting 2 from each value in the dat, we get
(3 + 8), (7 + 8), (1 + 8), (-2 + 8), (2 + 8), (6 + 8), (-3 + 8), (-5 + 8)
The data becomes 11, 15, 9, 6, 10, 14, 5, 3
Arranging the data in ascending order, we get
3, 5, 6, 9, 10, 11, 14, 15
Highest observation = 15
Lowest observation = 3
Range = 15 - 3
= 12
Therefore, the range remains the same in both the cases.
✦ Try This: The range of the data 5, 11, 2, –3, 2, 7, –4, –6 would change if 6 was added to 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 49
The range of the data 3, 7, 1, –2, 2, 6, –3, –5 would change if 8 was added to each value in the data. State whether the statement is true or false
Summary:
The given statement,”The range of the data 3, 7, 1, –2, 2, 6, –3, –5 would change if 8 was added to each value in the data” is false.
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