Twenty-five adults reported the amount of time each spent st : Integrated Reasoning (IR)
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Twenty-five adults reported the amount of time each spent st

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08 May 2013, 06:02
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Refer to the attached file.
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IR 4.docx [32.98 KiB]

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Re: Twenty-five adults reported the amount of time each spent st [#permalink]

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16 May 2013, 19:37
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1. To find the least possible mean the sum of all hours exercised must be the minimum.
For 0-1 hours lets assume all 5 exercised the minimum possible of just over 0 hours and same for all bars.
so SUM of hours exercised = 0*5 + 1*3+2*2+3*3+4*4+5*5+0+0+8*1+0+10*0 = 78
# respondents = 25
average = 78/25 = 3.12

2. # respondents who exercised on average <0.5 hours per day
If Avg hours exercised = 0.5 hours per day the Total hours exercised during the week will be 0.5*7 OR 3.5 hours/week
We need to count respondents who exercise below 3.5 hours per week.
That will include all in 0-1 hour, 1-2 hr, 2-3 hour and since 3.5 lies in between 3-4 band, we can take 2 cases:
CAse 1: where we assume all 4 in 3-4 years exercise MORE than 3.5 hours
Total # respondednts in that case = 5 + 3 + 2 + 4 = 14 (this is the maximum)
CAse 2: where we assume all 4 in 3-4 years exercise LESS than 3.5 hours
Total # respondednts in that case = 5 + 3 + 2 = 10 (this is the minimum)
Range od 10-14 respondents
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Re: Twenty-five adults reported the amount of time each spent st [#permalink]

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03 May 2014, 07:03
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srcc25anu wrote:
1. To find the least possible mean the sum of all hours exercised must be the minimum.
For 0-1 hours lets assume all 5 exercised the minimum possible of just over 0 hours and same for all bars.
so SUM of hours exercised = 0*5 + 1*3+2*2+3*3+4*4+5*5+0+0+8*1+0+10*0 = 78
# respondents = 25
average = 78/25 = 3.12

2. # respondents who exercised on average <0.5 hours per day
If Avg hours exercised = 0.5 hours per day the Total hours exercised during the week will be 0.5*7 OR 3.5 hours/week
We need to count respondents who exercise below 3.5 hours per week.
That will include all in 0-1 hour, 1-2 hr, 2-3 hour and since 3.5 lies in between 3-4 band, we can take 2 cases:
CAse 1: where we assume all 4 in 3-4 years exercise MORE than 3.5 hours
Total # respondednts in that case = 5 + 3 + 2 + 4 = 14 (this is the maximum)
CAse 2: where we assume all 4 in 3-4 years exercise LESS than 3.5 hours
Total # respondednts in that case = 5 + 3 + 2 = 10 (this is the minimum)
Range od 10-14 respondents

Thanks for the explanation! I fully understand the solution, but it took me almost 4 minutes to do it. Anyone know of a faster way to solve this question?

Thanks!
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Re: Twenty-five adults reported the amount of time each spent st [#permalink]

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23 May 2014, 04:16
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Hi Ashsim,

Part 1 Solution:

Sum of [Number of respondents * Least value of time spent in the range]
= 5*0 + 3*1 + 2*2 + 4*3 + 4*4 + 5*5 + 1*8 + 1*10
= 78

Average = $$\frac{78}{25} = 3.12$$

Part 2 Solution:

Less than 0.5 hr per day = less than 3.5 hr per week

Minimum number = 5 + 3 + 2 + 0 = 10 (When respondents spending time between 3 and 4 have values greater than 3.5)
Maximum Number = 5 + 3 + 2 + 4 = 14 (When respondents spending time between 3 and 4 have values less than 3.5)

I hope it could be solved in 2 mins

Rgds,
Rajat
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Re: Twenty-five adults reported the amount of time each spent st [#permalink]

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06 Aug 2014, 11:01
rajatjain14 wrote:
Hi Ashsim,

Part 1 Solution:

Sum of [Number of respondents * Least value of time spent in the range]
= 5*0 + 3*1 + 2*2 + 4*3 + 4*4 + 5*5 + 1*8 + 1*10
= 78

Average = $$\frac{78}{25} = 3.12$$

Part 2 Solution:

Less than 0.5 hr per day = less than 3.5 hr per week

Minimum number = 5 + 3 + 2 + 0 = 10 (When respondents spending time between 3 and 4 have values greater than 3.5)
Maximum Number = 5 + 3 + 2 + 4 = 14 (When respondents spending time between 3 and 4 have values less than 3.5)

I hope it could be solved in 2 mins

Rgds,
Rajat

Question : How do we know that less than 0.5 hr per day = less than 3.5 hr per week?
Re: Twenty-five adults reported the amount of time each spent st   [#permalink] 06 Aug 2014, 11:01
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