<u>The correct answer is </u><u>all of the above.</u>
Why is the range the most convenient measure of variability?
- Your data's spread from the lowest to the greatest value in the distribution is indicated by the range.
- The calculation of this variability index is the simplest.
- Simply subtract the lowest value from the highest value in the data set to determine the range.
How do you find the range?
- The difference between the lowest and highest values in a list or set is known as the range.
- Put all the numbers in order before determining the range. The lowest number should then be subtracted from the highest.
- The range of the list is provided in the response.
Learn more about range
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Using the dot product:
For any vector x, we have
||x|| = √(x • x)
This means that
||w|| = √(w • w)
… = √((u + z) • (u + z))
… = √((u • u) + (u • z) + (z • u) + (z • z))
… = √(||u||² + 2 (u • z) + ||z||²)
We have
u = ⟨2, 12⟩ ⇒ ||u|| = √(2² + 12²) = 2√37
z = ⟨-7, 5⟩ ⇒ ||z|| = √((-7)² + 5²) = √74
u • z = ⟨2, 12⟩ • ⟨-7, 5⟩ = -14 + 60 = 46
and so
||w|| = √((2√37)² + 2•46 + (√74)²)
… = √(4•37 + 2•46 + 74)
… = √314 ≈ 17.720
Alternatively, without mentioning the dot product,
w = u + z = ⟨2, 12⟩ + ⟨-7, 5⟩ = ⟨-5, 17⟩
and so
||w|| = √((-5)² + 17²) = √314 ≈ 17.720
