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# The median height of the 5 children in family A is 118

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The median height of the 5 children in family A is 118  [#permalink]

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09 Mar 2014, 06:38
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15% (low)

Question Stats:

85% (01:08) correct 15% (01:05) wrong based on 200 sessions

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The median height of the 5 children in family A is 118 cm. How many children in family A are taller than 128cm?

(1) The average height of the children in family A is 120cm.

(2) The second highest child in family A is 130cm.
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Re: The median height of the 5 children in family A is 118  [#permalink]

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09 Mar 2014, 06:51
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The median height of the 5 children in family A is 118 cm. How many children in family A are taller than 128cm?

The median of a set with odd (5) number of elements is the middle term, so we have that the heights in ascending order are {a, b, 118, c, d} ($$a\leq{b}\leq{118}\leq{c}\leq{d}$$)

(1) The average height of the children in family A is 120cm --> the sum of the heights is 120*5=600 cm:

If the heights are {10, 12, 118, 130, 130}, then 2 children are taller than 128 cm.
If the heights are {118, 118, 118, 122, 124}, then no child is taller than 128 cm.

Not sufficient.

(2) The second highest child in family A is 130cm --> c=130 --> $$a\leq{b}\leq{118}\leq{130}\leq{d}$$ --> 2 children, c and d, are taller than 128cm. Sufficient.

Theory on Statistics and Sets problems: math-standard-deviation-87905.html

All DS Statistics and Sets problems to practice: search.php?search_id=tag&tag_id=34
All PS Statistics and Sets problems to practice: search.php?search_id=tag&tag_id=55

Hope it helps.
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Re: The median height of the 5 children in family A is 118  [#permalink]

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09 Mar 2014, 10:56
We need to know whether 1, both, or neither of the last two spots is > 128.

Statement 1 only tells us the average. The distribution is not symmetric. The mean is pulled up by extreme values, but we have no idea how extreme. Insufficient.

Statement 2 tells us that both spots refer to children who are greater than 128 cm tall. Sufficient.

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Re: The median height of the 5 children in family A is 118  [#permalink]

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19 Nov 2017, 12:44
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Hi All,

We're told that the MEDIAN height of the 5 children in a family is 118 cm. We're asked for the number of children in that family are taller than 128cm. To start, since there are 5 children, the MEDIAN height will be the 3rd child (when the children are ordered from shortest to tallest). With a median of 118cm, there can be no more than 2 children who are taller than 128cm (so the answer to the question can only be 0, 1 or 2).

1) The average height of the children in family A is 120cm.

With an AVERAGE height of 120cm, the TOTAL height of all 5 children is (5)(120) = 600cm. We know that the median height is 118cm, but there are several possibilities.
IF... the children's heights are (in cm) are...
117, 117, 118, 124, 124 then the answer to the question is 0
111, 111, 118, 130, 130 then the answer to the question is 2
Fact 1 is INSUFFICIENT

2) The second highest child in family A is 130cm.

We already know that the median height is 118cm. Fact 2 tells us that the second-tallest child is 130cm, thus the tallest child must be AT LEAST 130cm. Therefore, we know that 2 of the children ARE taller than 128cm and there are no other options.
Fact 2 is SUFFICIENT

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Re: The median height of the 5 children in family A is 118  [#permalink]

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06 Dec 2018, 08:24
The median height of the 5 children in family A is 118 cm. How many children in family A are taller than 128cm?

Make a list of the set A

Child -> 1 2 3 4 5
Hgt -> ? ? 118 ? ?

(1) The average height of the children in family A is 120cm.

1,2,3 are under 118cm, but child 4 could be 127 and child 5 could be 150 or any number that would make the average 120. So multiple combinations for child 4 & 5 insufficient.

(2) The second highest child in family A is 130cm.

Look at your list, if 4 is 130cm then the 5th child must be taller than 128cm,

B is sufficient
Re: The median height of the 5 children in family A is 118 &nbs [#permalink] 06 Dec 2018, 08:24
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