Range (Statistics) Math Example 4

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Example 4

hard
A data set has a range of 24. If the maximum value is 3x+53x + 5 and the minimum value is x−3x - 3, find the value of xx.

Solution

  1. 1
    Set up the equation: Range=max⁡−min⁡\text{Range} = \max - \min
  2. 2
    Substitute: (3x+5)−(x−3)=24(3x + 5) - (x - 3) = 24
  3. 3
    Simplify: 3x+5−x+3=24⇒2x+8=243x + 5 - x + 3 = 24 \Rightarrow 2x + 8 = 24
  4. 4
    Solve: 2x=16⇒x=82x = 16 \Rightarrow x = 8

Answer

x=8x = 8
By translating the word problem into an algebraic equation using the range formula, we can solve for the unknown. Always verify: max = 29, min = 5, range = 24. Confirmed correct.

About Range (Statistics)

The statistical range is the difference between the maximum and minimum values in a data set: range=max⁡−min⁡\text{range} = \max - \min.

Learn more about Range (Statistics) →

More Range (Statistics) Examples

Example 1 easy

Find the range of the data set: [formula].

Example 2 medium

Two classes took the same test. Class A scores: [formula]. Class B scores: [formula]. Compare the ra

Example 3 easy

Find the range of the monthly temperatures (°F): [formula].

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