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Maths

Discrete and continuous measurements

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Limits of accuracy - discrete measures

Number recordings are not always exact, and in some cases they may be rounded up.

When a number has been recorded to a certain accuracy - for instance, the nearest 1cm or the closest 10 - you can work out its highest and lowest possible values according to the limits of accuracy provided.

These outcomes are often referred to as an upper or lower bound.

Question

Mary's height is given as 162cm, correct to the nearest cm. Between which limits does Mary's height lie?

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Answer
image: triangle, left side measures 2.4cm and the base 3.7cm, a right angle is marked in relation to the left side and base.

161.5 is the smallest number which rounds up to 162. 162.5 is the smallest number which rounds up to 163. Therefore, Mary's height must be below 162.5cm. (But remember that it could be 162.4999999999999... cm)

We say that

161.5 cm less than or equal to Mary's height < 162.5cm.

The lower limit is 161.5cm. The upper limit is 162.5cm.

Sometimes in examinations they ask for the highest and smallest values, or the upper and lower bounds, for continuous data they are the same.

Now try this one.

Question

people on the bus

The number of people on a bus is given as 50, correct to the nearest 10. What is the lowest and highest possible number of people on the bus?

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Answer

The number 50 is correct to the nearest 10.

Looking at the number line, we can see that 45 is the smallest possible number closest to 50 when rounding up, and 54 is the largest possible number closest to 50 when rounding down.

So the lower bound is 45, and the upper bound is 54. Therefore, the number of people on the bus can be any number between 45 and 54.

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