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# For a sample of 210 households, one-third of the households

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For a sample of 210 households, one-third of the households [#permalink]  11 Dec 2017, 10:04
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72% (01:06) correct 27% (00:39) wrong based on 18 sessions
For a sample of 210 households, one-third of the households do not have any pets, one-third of the households each have 1 pet, and the rest of the households each have 2 pets. Which of the following statistics for the sample are equal to 1?

Indicate $$all$$ such statistics.

A. The average (arithmetic mean) number of pets per household.
B. The median number of pets per household.
C. The range of the numbers of pets per household.
[Reveal] Spoiler: OA

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Director
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Kudos [?]: 621 [1] , given: 88

Re: For a sample of 210 households, one-third of the households [#permalink]  15 Jan 2018, 21:37
1
KUDOS
total number of household=210
no pet household = 1/3*210 = 70
1 pet household = 1/3*210 = 70
2 pet household = 210-(70+70) = 70
avg = total pets/number of household
70*1 + 70*2 + 70*0)/210 = 1
median = 211/2 = 105.5th term
data in ascending order is in the form
0,0,0,0,0,.....0(70st term)
1(71st term),1,1,1,1,.....1(140th term)
as such 105.5th term= (1+1)/2 = 1
Highest number of pet per household - lowest number of pet per household= 2-0 =2
(a,b)
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This is my response to the question and may be incorrect. Feel free to rectify any mistakes

Intern
Joined: 26 Mar 2017
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WE: Account Management (Internet and New Media)
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Kudos [?]: 12 [0], given: 53

Re: For a sample of 210 households, one-third of the households [#permalink]  14 Nov 2018, 09:06
amorphous wrote:
total number of household=210
no pet household = 1/3*210 = 70
1 pet household = 1/3*210 = 70
2 pet household = 210-(70+70) = 70
avg = total pets/number of household
70*1 + 70*2 + 70*0)/210 = 1
median = 211/2 = 105.5th term
data in ascending order is in the form
0,0,0,0,0,.....0(70st term)
1(71st term),1,1,1,1,.....1(140th term)
as such 105.5th term= (1+1)/2 = 1
Highest number of pet per household - lowest number of pet per household= 2-0 =2
(a,b)

Hi,

Please explain the median part of the calculation. I didn't understand the 211/2 = 105.5. How did we get 211? I didn't get the entire logic behind it.
Director
Joined: 07 Jan 2018
Posts: 659
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Kudos [?]: 621 [3] , given: 88

Re: For a sample of 210 households, one-third of the households [#permalink]  15 Nov 2018, 07:04
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median is the middlemost value.
There are in total 210 data
If we arrange this data in ascending order we get
70 zero's followed by 70 one's and finally 70 two's
the formula for median is $$\frac{(n+1)}{2}$$
There are 210 data so our median is $$\frac{211}{2}$$ which is the 105.5 th term
the median is therefore $$\frac{(1+1)}{2}$$ = 1
_________________

This is my response to the question and may be incorrect. Feel free to rectify any mistakes

Intern
Joined: 26 Mar 2017
Posts: 23
WE: Account Management (Internet and New Media)
Followers: 0

Kudos [?]: 12 [0], given: 53

Re: For a sample of 210 households, one-third of the households [#permalink]  15 Nov 2018, 21:03
amorphous wrote:
median is the middlemost value.
There are in total 210 data
If we arrange this data in ascending order we get
70 zero's followed by 70 one's and finally 70 two's
the formula for median is $$\frac{(n+1)}{2}$$
There are 210 data so our median is $$\frac{211}{2}$$ which is the 105.5 th term
the median is therefore $$\frac{(1+1)}{2}$$ = 1

Thanks a lot for the prompt revert. I understood.
Re: For a sample of 210 households, one-third of the households   [#permalink] 15 Nov 2018, 21:03
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