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Dropdown 1: 3.12
Dropdown 2: 10 and 14
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Difficulty:
95%
(hard)
Question Stats:
30% (03:07) correct
70%
(03:22)
wrong
based on 2198
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Twenty-five adults reported the amount of time each spent exercising during a particular week. The results are summarized in the graph as follows: 5 respondents reported exercising for less than 1 hour, 3 respondents reported exercising for at least 1 hour but less than 2, and so on.
Based on the given information, use the drop-down menus to most accurately complete the following statements.
The least possible value for the mean of the numbers of hours of exercise reported for the week is .
The number of respondents who exercised on average less than one-half hour per day during the week is between , inclusive.
ID: 100406
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Dropdown 1: 3.12
Dropdown 2: 10 and 14
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16 May 2013, 20:37
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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
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
23 May 2014, 05:16
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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
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
