Please help with this one!!
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essex-mum18
- Posts: 218
- Joined: Sun Nov 25, 2007 12:09 am
Please help with this one!!
If a number is rounded I can find the possible error
The following was taken from a sports article
“There was a capacity crowd at the stadium of 3400. In just the first 3 minutes a goal was scored. “
Given that the capacity was to the nearest 100, how many people could there have been at the match?
Given that the time was given to the nearest minute, when could the goal have been scored?
Thanks in advance
The following was taken from a sports article
“There was a capacity crowd at the stadium of 3400. In just the first 3 minutes a goal was scored. “
Given that the capacity was to the nearest 100, how many people could there have been at the match?
Given that the time was given to the nearest minute, when could the goal have been scored?
Thanks in advance
My reasoning is that anywhere between 3400 and 3449 people could have been there as if there were 3450 then it would have been rounded to 3500.
The time one is more challenging though as there are 60 seconds but I think it would be anywhere between 3 mins 0 seconds to 3 mins 29 seconds but cannot be 100% sure.
Deb
The time one is more challenging though as there are 60 seconds but I think it would be anywhere between 3 mins 0 seconds to 3 mins 29 seconds but cannot be 100% sure.
Deb
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essex-mum18
- Posts: 218
- Joined: Sun Nov 25, 2007 12:09 am
Rounding numbers
The crowd size could be anywhere between 3351 and 3449, because 3351 is closer to 3400 than it is to 3300, and 3449 is closer to 3400 than it is to 3500.
The numbers 3350 and 3450 are exactly halfway between the "whole" hundreds either side of them and could therefore go either way if rounded. As the question doesn't specify rounding up or down, this introduces an ambiguity and those numbers cannot be included in the definite range that can be rounded to 3400.
For the goal scoring, the time frame is from 2'31" to 3'29", both times being closer to 3" than to 2" and 4" respectively. The times 2'30" and 3'30" suffer from the same ambiguity as in the crowd numbers and should not be included in the possible range of times.
I think that's it.
The numbers 3350 and 3450 are exactly halfway between the "whole" hundreds either side of them and could therefore go either way if rounded. As the question doesn't specify rounding up or down, this introduces an ambiguity and those numbers cannot be included in the definite range that can be rounded to 3400.
For the goal scoring, the time frame is from 2'31" to 3'29", both times being closer to 3" than to 2" and 4" respectively. The times 2'30" and 3'30" suffer from the same ambiguity as in the crowd numbers and should not be included in the possible range of times.
I think that's it.
How pedantic do you want to get in reading the question :-)
Following the usual rounding conventions
3350 - 3449 in the stadium plus the requisite number of players for the sport and hangers-on.
0 - 3 Mins 29.999999999999999 seconds - to the nearest femto second and assuming 'goals' in this sport can be scored in an arbitrarily short time.
It is an error though to assume the goal could not have been scored in, say, the first second.
Following the usual rounding conventions
3350 - 3449 in the stadium plus the requisite number of players for the sport and hangers-on.
0 - 3 Mins 29.999999999999999 seconds - to the nearest femto second and assuming 'goals' in this sport can be scored in an arbitrarily short time.
It is an error though to assume the goal could not have been scored in, say, the first second.
Rounding numbers
Only sufficient pedantry to be accurate. The "crowd" is generally understood to be the spectators only.
The question states that the score happened within 3 minutes - to the nearest minute. 3 minutes to the nearest minute is any time from 2'31" to 3'29". Whilst the question does say "in the first three minutes", which could be taken as at any time from kick off up to a time from 2'31" to 3'29", that is unlikely to be what it means.
A score in the 37th minute would not be described as being within 50 minutes, unless the writer belonged to a strange sect where 50 minute time spans were significant. It would be described (if using approximation) as being within 40 minutes. With such a small and precise time as 3 minutes, this report is much more likely to be referring to 3 minutes as the precise time of score (to the nearest minute) and had it meant that the score had been at the 2 minute point or within a split second of kick off, it would have said "in the first two minutes", "in the first minute" or "immediately from kick-off". It is clear that the meaning to be construed to the question is that the score was within 29 seconds either side of the 3 minute point.
As for the mid-point between values, it is correct that there is a rounding convention that x.5 rounds up to the next whole number (in the absence of instructions to the contrary), but I don't know if Year 6 pupils are expected to know it.
The question states that the score happened within 3 minutes - to the nearest minute. 3 minutes to the nearest minute is any time from 2'31" to 3'29". Whilst the question does say "in the first three minutes", which could be taken as at any time from kick off up to a time from 2'31" to 3'29", that is unlikely to be what it means.
A score in the 37th minute would not be described as being within 50 minutes, unless the writer belonged to a strange sect where 50 minute time spans were significant. It would be described (if using approximation) as being within 40 minutes. With such a small and precise time as 3 minutes, this report is much more likely to be referring to 3 minutes as the precise time of score (to the nearest minute) and had it meant that the score had been at the 2 minute point or within a split second of kick off, it would have said "in the first two minutes", "in the first minute" or "immediately from kick-off". It is clear that the meaning to be construed to the question is that the score was within 29 seconds either side of the 3 minute point.
As for the mid-point between values, it is correct that there is a rounding convention that x.5 rounds up to the next whole number (in the absence of instructions to the contrary), but I don't know if Year 6 pupils are expected to know it.
