# Error in Measurement Sheet. - Upper limits - HELP!!

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• Jan 21st 2007, 09:37 AM
6Brandon6
Error in Measurement Sheet. - Upper limits - HELP!!
Ok, I've been dumped with a maths sheet, which I don't have a clue about and I don't even know what it's about. If anyone could give me the answers and help me with the questions you don't know how much I'd appreciate it.

1. The weights of four rowers are 86.3kg, 89.2kg, 85.0 kg and 93.9 kg.
a) Find the upper limit of their total weight
b) Use the answer to a) to find the maximum value of the mean weight
c) Find the minimum value of the mean weight.

2. A room is 3.93 m long and 2.89 m wide correct to the nearest centimetre. Find the lower and upper limits of the area of the room.

There's alot more but could I have help on those for a starter?
Thanks in advance.
• Jan 21st 2007, 10:41 AM
Soroban
Hello, 6Brandon6!

They are talking about Accuracy and Rounding.

Quote:

1. The weights of four rowers are 86.3 kg, 89.2 kg, 85.0 kg and 93.9 kg.

a) Find the upper limit of their total weight

We assume they rounded the weights to the nearest tenth of a kilogram.

The weight of Rower #1 was given as $\displaystyle 86.3$ kg.
His actual weight must be less than $\displaystyle 86.35$ kg.
If his weight was exactly $\displaystyle 86.35$, it would have been rounded up to $\displaystyle 86.4$ kg.
. . So we have: .$\displaystyle W_1 < 86.35$ [1]

The weight of Rower #2 was given as $\displaystyle 89.2$ kg.
. . So we have: .$\displaystyle W_2 < 89.25$ [2]

The weight of Rower #3 was given as $\displaystyle 89.0$ kg.
. . So we have: .$\displaystyle W_3 < 89.05$ [3]

The weight of Rower #4 was given as $\displaystyle 94.9$ kg.
. . So we have: .$\displaystyle W_4 < 93.95$ [4]

Adding [1], [2], [3], [4], we have: .$\displaystyle W_1 + W_2 + W_3 + W_4 \:< \:358.6$ kg.

Therefore, the upper limit of their total weight is $\displaystyle 358.6$ kg.

Quote:

b) Use the answer to a) to find the maximum value of the mean weight

We have: .$\displaystyle \frac{358.6}{4}\:=\:89.65$

Therefore, the maximum value of their mean (average) weight is: $\displaystyle 89.65$ kg.

Quote:

c) Find the minimum value of the mean weight.

The weight of Rower #1 was given as $\displaystyle 86.3$ kg.
His actual weight must be greater than or equal to $\displaystyle 86.25$ kg.
If his weight was less than $\displaystyle 86.25$, it would have been rounded down to $\displaystyle 86.2$
. . So we have:\ .$\displaystyle W_1 \geq 86.25$

. . . . Similarly: .$\displaystyle \begin{array}{ccc}W_2 \geq 89.15 \\ W_3 \geq 84.95 \\ W_4 \geq 93.85\end{array}$

Hence: .$\displaystyle W_1 + W_2 + W_3 + W_4 \:\geq\:354.2$

Therefore, the minimum value for their mean weight is: .$\displaystyle \frac{354.2}{4}\:=\:88.55$ kg.

• Jan 21st 2007, 11:35 AM
6Brandon6
Thanks mate.
Had a crack at it before your post, seemed I had a rough idea. But now I know fully. Cheers again.