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how to find the range

To find the range in math, you look at how far your data stretch from the smallest value to the largest value.

Quick Scoop: What “range” means

  • The range is a measure of spread: it tells you how wide the gap is between the lowest and highest numbers in a set.
  • In symbols:
    Range=maximum value−minimum value\text{Range}=\text{maximum value}-\text{minimum value}Range=maximum value−minimum value.
  • A small range means your data are tightly packed; a large range means they’re more spread out.

Step‑by‑step: How to find the range of a data set

Imagine you’re given test scores: 72, 85, 90, 68, 95.

  1. List or scan the data
    • It helps (but isn’t required) to rewrite them in order from smallest to largest: 68, 72, 85, 90, 95.
  1. Find the minimum
    • The minimum is the smallest number in the set.
    • Here, the minimum is 68.
  1. Find the maximum
    • The maximum is the largest number in the set.
    • Here, the maximum is 95.
  1. Subtract minimum from maximum
    • Range=95−68=27\text{Range}=95-68=27Range=95−68=27.
 * So the range of these scores is 27 points.

In words: “Take the biggest value, subtract the smallest value; the answer is the range.”

Another quick example

Data: 8, 11, 12, 15, 19, 22, 25.

  • Minimum = 8
  • Maximum = 25
  • Range=25−8=17\text{Range}=25-8=17Range=25−8=17.

So the range is 17. That tells you the data span 17 units from lowest to highest.

Range for functions (brief peek)

Sometimes “range” means “all possible output values of a function.”

  • For a function like y=f(x)y=f(x)y=f(x), the range is all the yyy-values the function can produce.
  • A common way to see this is by looking at the graph vertically: how low the graph goes and how high it goes on the yyy-axis.

Example idea (not full computation): For a U‑shaped quadratic like y=3x2+6x−2y=3x^2+6x-2y=3x2+6x−2, the graph has a lowest point (a vertex) and then goes up forever; the range starts at that lowest yyy-value and extends upward.

Mini tips and common mistakes

  • Always double‑check the min and max. Missing one value will give the wrong range.
  • Ordering helps. Putting numbers in ascending order makes it easy to see the smallest and largest.
  • Negative numbers work the same way. Even if numbers are negative, you still do “biggest minus smallest.”
  • Range is just one summary. It’s useful but simple; it doesn’t show what’s happening in the middle of the data like the mean or median.

Tiny TL;DR

  • Find the smallest number (min).
  • Find the largest number (max).
  • Do: Range=max−min\text{Range}=\text{max}-\text{min}Range=max−min.

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