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What You Need to Know About Ranges

The range of a set of values is a really useful description of a list to show how spread out the values are – or the difference between the biggest and the smallest values.

You often use a range when comparing two data sets – for example, ‘Team A had a slightly lower average than Team B, but Team A’s range was far smaller. Therefore Team A is much more reliable.’

How to calculate range

Working out the range of a set of numbers is pretty straightforward. Here’s what you do:

  1. Find the biggest number.

  2. Find the smallest number.

  3. Take the smallest away from the biggest.

    The answer is your range.

The only slightly tricky thing is picking out the biggest and smallest numbers from an unordered list, but putting numbers into order isn’t much of a challenge. Alternatively, find a relatively big number in the list that jumps out at you and then go through the list and see whether any other numbers are bigger than it; then you do just the same thing for small numbers.

If you’re lucky, a question in your exam may simply say ‘Ellen’s best golf score was 70 and her worst score was 85. What was the range of her scores?’ You take the smaller number (70) away from the bigger number (85) and get a range of 15.

Don’t overcomplicate things! Just look for the simplest thing that could possibly work.

More frequently, the examiner gives you a list of numbers and asks you to find the range. Let’s use the following list of numbers: 1, 2, 1, 1, 0, 2, 1, 0, 3, 4, 2, 1, 1, 1, 3, 4, 4. The biggest number in the list is 4. The smallest number is 0. The range is 4 – 0 = 4.

Occasionally the examiner gives you a big table of numbers and asks you to find the range of the table. This is no different from finding the range of a list of numbers: you find the biggest and smallest numbers in the table and take them away as usual.

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For example, the biggest number in this table is 684, and the smallest number is 509. When you take them away, you get 175, which is the range of the data.

Rightly or wrongly, examiners think of range as a fairly easy calculation, and some try to compensate by making the questions harder. If you have a complicated table, make sure you look at the right values and check you have the highest and lowest numbers.

Pull the range out of a graph

You may need to find the range of data given in a graph. As long as you’re comfortable reading values from a graph you’re all set. Here’s what you do:

  1. Find the highest value on the graph.

    Look for the value of the tallest bar or the highest point on a line graph.

  2. Find the lowest value on the graph.

    Look for the value of the smallest bar or the lowest point.

  3. Take the value from Step 2 away from the value in Step 1.

    The answer is your range.

The only difference is you pull the relevant numbers from the graph before you do the taking-away sum. In the example, the highest temperature recorded in the graph is 18ºC and the lowest temperature is 11ºC. The range of these two temperatures is simply 18 – 11 = 7 degrees.

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