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For a sample of 210 households, one-third of the households do not hav

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Bunuel
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For a sample of 210 households, one-third of the households do not hav [#permalink] For a sample of 210 households, one-third of the households do not hav   23 May 2019, 02:48
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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?

I. The average (arithmetic mean) number of pets per household.
II. The median number of pets per household.
III. The range of the numbers of pets per household.

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III
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D
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Re: For a sample of 210 households, one-third of the households do not hav [#permalink] For a sample of 210 households, one-third of the households do not hav   23 May 2019, 06:47
70 - 0 pets
70 - 1 pet
70 - 2 pet

1) Average = 70*2+70*1+70*0/210 = 210/210 = 1
True

2) Median = {0,1,2}
True

3) Range = 2-0 = 2
False

Only 1 and 2 are true

D is the answer.
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Re: For a sample of 210 households, one-third of the households do not hav [#permalink] For a sample of 210 households, one-third of the households do not hav   23 May 2019, 07:06
Is okay to simplify part I. to the following using weighted average concept? Rather than even using the 210 #.

1/3*0 + 1/3*1 + 1/3*2 = 0 + 1/3 + 2/3 = 1

For median, this assumes normal distribution so median must be in middle group (1)?

That's how I thought about it to minimize the actual work needed to answer it.
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Re: For a sample of 210 households, one-third of the households do not hav [#permalink] For a sample of 210 households, one-third of the households do not hav   27 May 2019, 19:12
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Bunuel wrote:
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?

I. The average (arithmetic mean) number of pets per household.
II. The median number of pets per household.
III. The range of the numbers of pets per household.

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III


So we see that 1/3 has zero, 1/3 have one, and 1/3 have two pets.

So the average is [70(0) + 70(1) + 70(2)]/210 = 210/210 = 1

We also see that the median must be 1; however, the range is 2 - 0 = 2.

Answer: D
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Re: For a sample of 210 households, one-third of the households do not hav [#permalink]
27 May 2019, 19:12
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