Error-Intervals Aqa Foundation

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Exam code:8300

Error intervals

What is an error interval?

An error interval is the range of possibles values that a number could have been before it was rounded or truncated

How do we find the error interval for a rounded number?

Think about the smallest and biggest numbers that a value could be before they round up to the next value or down to the previous value
You may be given a question where the number has been rounded to a given degree of accuracy
- E.g. A stick has a length, $l$ , of 5 cm correct to the nearest whole number
  - It could have been as short as 4.5 cm and still been rounded up to 5 cm
  - It could have been up to (but not including) 5.5 cm before it was rounded down to 5 cm
  - The error interval for the length of the stick is $4.5 less or equal than l less than 5.5$
The rounded value should be the midpoint of the error interval

How do we find the error interval for a truncated number?

You may be given a question where the number has been truncated
- E.g. The first 3 digits of an answer, $a$ , to a calculation have been written down as 2.95
  - The smallest value that the answer could have been is 2.95
  - The largest value that the number could have been up to (but not equal to) is 2.96 before it was truncated to 2.95
  - The error interval for the size of the number is $2.95 less or equal than a less than 2.96$
The truncated value should be the same as the smallest value in the error interval

Examiner Tips and Tricks

Read the exam question carefully to correctly identify the degree of accuracy.
- It may be given as a place value, e.g. rounded to 1 s.f., or it may be given as a measure, e.g. nearest metre or it may have been truncated.

Worked Example

The length of a road, $l$ km, is given as $l equals 3.6$ , correct to 1 decimal place.

Write down the error interval for <img alt=”l.” data-mathml='<math ><semantics><mrow><mi>l</mi><mo>.</mo></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true}</annotation></semantics></math>’ height=”22″ role=”math” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2222%22%20width%3D%2212%22%20wrs%3Abaseline%3D%2216%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3El%3C%2Fmi%3E%3Cmo%3E.%3C%2Fmo%3E%3C%2Fmath%3E–%3E%3Cdefs%3E%3Cstyle%20type%3D%22text%2Fcss%22%3E%40font-face%7Bfont-family%3A’math1d9d4f495e875a2e075a1a4a6e1’%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMi7iBBMAAADMAAAATmNtYXDEvmKUAAABHAAAADRjdnQgDVUNBwAAAVAAAAA6Z2x5ZoPi2VsAAAGMAAAAbmhlYWQQC2qxAAAB%2FAAAADZoaGVhCGsXSAAAAjQAAAAkaG10eE2rRkcAAAJYAAAACGxvY2EAHTwYAAACYAAAAAxtYXhwBT0FPgAAAmwAAAAgbmFtZaBxlY4AAAKMAAABn3Bvc3QB9wD6AAAELAAAACBwcmVwa1uragAABEwAAAAUAAADSwGQAAUAAAQABAAAAAAABAAEAAAAAAAAAQEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAgICAAAAAg1UADev96AAAD6ACWAAAAAAACAAEAAQAAABQAAwABAAAAFAAEACAAAAAEAAQAAQAAAC7%2F%2FwAAAC7%2F%2F%2F%2FTAAEAAAAAAAABVAMsAIABAABWACoCWAIeAQ4BLAIsAFoBgAKAAKAA1ACAAAAAAAAAACsAVQCAAKsA1QEAASsABwAAAAIAVQAAAwADqwADAAcAADMRIRElIREhVQKr%2FasCAP4AA6v8VVUDAAABACAAAACgAIAAAwAvGAGwBBCwA9SwAxCwAtSwAxCwADywAhCwATwAsAQQsAPUsAMQsAI8sAAQsAE8MDE3MxUjIICAgIAAAAABAAAAAQAA1XjOQV8PPPUAAwQA%2F%2F%2F%2F%2F9Y6E3P%2F%2F%2F%2F%2F1joTcwAA%2FyAEgAOrAAAACgACAAEAAAAAAAEAAAPo%2F2oAABdwAAD%2FtgSAAAEAAAAAAAAAAAAAAAAAAAACA1IAVQDIACAAAAAAAAAAKAAAAG4AAQAAAAIAXgAFAAAAAAACAIAEAAAAAAAEAADeAAAAAAAAABUBAgAAAAAAAAABABIAAAAAAAAAAAACAA4AEgAAAAAAAAADADAAIAAAAAAAAAAEABIAUAAAAAAAAAAFABYAYgAAAAAAAAAGAAkAeAAAAAAAAAAIABwAgQABAAAAAAABABIAAAABAAAAAAACAA4AEgABAAAAAAADADAAIAABAAAAAAAEABIAUAABAAAAAAAFABYAYgABAAAAAAAGAAkAeAABAAAAAAAIABwAgQADAAEECQABABIAAAADAAEECQACAA4AEgADAAEECQADADAAIAADAAEECQAEABIAUAADAAEECQAFABYAYgADAAEECQAGAAkAeAADAAEECQAIABwAgQBNAGEAdABoACAARgBvAG4AdABSAGUAZwB1AGwAYQByAE0AYQB0AGgAcwAgAEYAbwByACAATQBvAHIAZQAgAE0AYQB0AGgAIABGAG8AbgB0AE0AYQB0AGgAIABGAG8AbgB0AFYAZQByAHMAaQBvAG4AIAAxAC4AME1hdGhfRm9udABNAGEAdABoAHMAIABGAG8AcgAgAE0AbwByAGUAAAMAAAAAAAAB9AD6AAAAAAAAAAAAAAAAAAAAAAAAAAC5BxEAAI2FGACyAAAAFRQTsQABPw%3D%3D)format(‘truetype’)%3Bfont-weight%3Anormal%3Bfont-style%3Anormal%3B%7D%3C%2Fstyle%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Times%20New%20Roman%22%20font-size%3D%2218%22%20font-style%3D%22italic%22%20text-anchor%3D%22middle%22%20x%3D%222.5%22%20y%3D%2216%22%3El%3C%2Ftext%3E%3Ctext%20font-family%3D%22math1d9d4f495e875a2e075a1a4a6e1%22

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