Ind maths question - can anyone suggest an easy method

[teacher_mum]

Question from an independent school paper

Because she is sick in bed and has nothing better to do . Amy counts the number of buses which go past her house in every two minute period. She gets the following results.

Number of buses

0 1 2 3 4 5 6
Periods in which this number pass

15 17 12 6 6 5 1

i) How many buses did she count ?
ii) How long, at least would this have take her ?
iii) What is the most likely number of buses to pass Amy’s house in any two minute period?


Thank you in advance

[muksoni]

a) how many buses did she count?

Add busses in each period.

0x15=0
+
1x17=17
+
2x12=24
+
3x6=18
+
4x6=24
+
5x5=25
+
6x1=6

= 114 buses.

How long would it have taken?
= (Total number of periods) x (duration of each period)
= (15+17+12+6+6+5+1) x (2 minutes)
= 62 x 2
= 124 minutes

Most likely number of buses in any period?

= 1 (because it happened 17 times)

hope this helps.

regards.

[mystery]

Uh? I'm assuming the layout went wonky and the question is telling us that in 15 two minute periods 0 buses went past, in 17 2 minute periods 1 bus went past, in 12 2 minute periods 3 buses went past etc etc.

So the number of buses she counted was 15x0 plus 17 x 1 plus 12 x 2 etc etc.

How long, at least, did this take her - well each period was 2 minutes and she counted for 15+17+12+6+6+5+1 periods. Then multiply the number of periods by 2 minutes.

Most likely number of buses to pass is 1, as this is the number that went past during 17 of the time periods, and 1 is the number that occurred most frequently as 17 is the highest number of periods to have the same number of buses passing.

Hope that makes sense.

[mystery]

Oops someone else replied at same time as me!!

[teacher_mum]

Hello

Thank you to both of you The tabulation didn't work out - sorry.