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The World Health Organization (WHO) has produced a comprehensive set o

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The World Health Organization (WHO) has produced a comprehensive set o [#permalink] New post  Updated on: 06 Oct 2023, 06:26
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The World Health Organization (WHO) has produced a comprehensive set of growth standards for children. These standards are based on studies of children living in 6 nations on 5 continents under optimal conditions with respect to health and nutrition. The table displays the percentile distribution of height, in centimeters, at 3-month intervals, for boys ages 2 through 5 according to the WHO model. In a model population -- a large population of boys ages 2 through 5 that conforms to the WHO growth standards -- for n = 3, 15, 50, 85, and 97, nth percentile in height for a given age is the unique height among boys of that age that is greater than or equal to n percent, and less than or equal to (100- n) percent, of heights of boys of that age.
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1. For each of the following statements, select Yes if the statement must be true of a boy selected at random from a model population. Otherwise, select No.
Yes No
If his age is greater than 3 years 3 months, the probability that his height is at least 98.0 cm is greater than 50%.
If he is at least 105 cm tall, the probability that his weight is 14.0 kg is no greater than 3%
If he is 114 cm tall, he is taller than at least 85% of boys his age.
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2. Consider an individual boy from a model population. Suppose that from age 2 through age 5, this boy's weight is at the 97th percentile for his height and his height is at the 97th percentile for his age. Which one of the following statements must be true of the boy at age 5 years 0 months?
His age is at the 97th percentile for his height.
His weight is at the 97th percentile for his age.
His height is at the 97th percentile for his weight.
His weight is approximately 166% of his weight at age 2 years 0 months.
His weight is approximately 197% of his weight at age 2 years 0 months.
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3. B is a boy aged 4 years 3 months whose height is 110 cm and whose weight is 19 kg. For each of the following statements, select Yes if, based on the given information, it must be true of B relative to a model population. Otherwise, select No.
Yes No
Approximately 50% of boys at the same weight are shorter than B.
No more than 15% of boys at this age are taller than B.
B's height is greater than or equal to that of 50% of boys aged 5 years 0 months.
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4. B is a boy aged 4 years 3 months whose height is 110 cm and whose weight is 19 kg. For each of the following statements, select Yes if, based on the given information, it must be true of B relative to a model population. Otherwise, select No.
Yes No
At least 15% of boys at the same height have a weight that is less than or equal to that of B
At least 80% of boys at this age have heights within 10% of B's height.
B's height is less than that of at most 3% of boys at age 4 years 0 months.
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5. For each of the following statements, select Yes if the statement must be true of a boy selected at random from a model population. Otherwise, select No.
Yes No
If his age is exactly 4 years 0 months, the probability that his height is at exactly 99.0 cm is 15%
If he is 81 cm tall, he is shorter than at least 95% of boys his age.
If he is 120 cm tall, he weighs more than 97% of boys age 2 years 6 months.
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6. Consider an individual boy from a model population. Suppose that from age 2 through age 5, this boy’s weight is at the 50th percentile for his height and his height is at the 50th percentile for his age. Which one of the following statements must be true of the boy at age 5 years 0 months?
His age is at the 50th percentile for his height.
His weight is at the 50th percentile for his age.
His height is at the 50th percentile for his weight.
His weight is approximately 150% of his weight at age 2 years 0 months.
His weight is approximately 200% of his weight at age 2 years 0 months.
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Originally posted by maybeam on 15 Jul 2012, 07:01.
Last edited by BottomJee on 06 Oct 2023, 06:26, edited 9 times in total.
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Re: The World Health Organization (WHO) has produced a comprehensive set o [#permalink] New post  23 Jul 2012, 13:26
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The World Health Organization (WHO) has produced a comprehensive set of growth standards for children. These standards are based on studies of children living in 6 nations on 5 continents under optimal conditions with respect to health and nutrition.
Height-for-age
The table displays the percentil distribution of height, in centimeters, at 3-month intervals, for boys ages 2 through 5 according to the WHO model. In a model population -- a large population of boys ages 2 through 5 that conforms to the WHO growth standards -- for n = 3, 15, 50, 85, and 97, nth percentile in height for a given age is the unique height among boys of that age that is greater than or equal to n percent, and less than or equal to (100- n) percent, of heights of boys of that age
Attachment:
attach1.JPG
attach1.JPG [ 76.53 KiB | Viewed 23297 times ]


Weight-for-height
Attachment:
attach1.JPG
attach1.JPG [ 54.7 KiB | Viewed 23297 times ]

The graph shows the percentile distribution of weight, in kilograms, for heights from 80 cm to 120 cm, for boys ages 2 through 5, according to the WHO model. In a model population, for n = 3, 15, 50, 85, and 97, the nth percentile in weight for a given heigh is the unique weight among boys of that height that is greater than or equal to n percent, and less than or equal to (100 - n) percent, of weights of boys of that height.

For each of the following statements, select Yes if the statement must be true of a boy selected at random from a model population. Otherwise, select No.

A If his age is exactly 4 years 0 months, the probability that his height is at exactly 99.0 cm is 15%
B. If he is 81 cm tall, he is shorter than at least 95% of boys his age.
C. If he is 120 cm tall, he weighs more than 97% of boys age 2 years 6 months.

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A.no
B. yes
C. no
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Re: The World Health Organization (WHO) has produced a comprehensive set o [#permalink] New post  10 Sep 2021, 13:02
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Official Explanation


1. For each of the following statements, select Yes if the statement must be true of a boy selected at random from a model population. Otherwise, select No.

Using the table in Height-for-age standards, the 50th percentile height for boys aged 3 years 3 months is 98.0 cm, so 50% of boys this age are taller than this. For boys aged 3 years 6 months and older, the 50th percentile height is greater than 98.0 cm, so at least 50% of boys this age are taller than this. Moreover, for boys 4 years 0 months and older, the 15th percentile height exceeds 98.0 cm, so at these ages, at least 85% of boys are taller than 98.0 cm. Thus, for a boy selected at random from a model population whose age is greater than 3 years 3 months, the probability that his height is at least 98.0 cm is greater than 50%.

The correct answer is Yes.

Using Weight-for-height standards, the 3rd percentile weight for height 105 cm is just over 14 kg, and for heights greater than 105 cm, the 3rd percentile weight is greater than 14 kg. Thus, at most, 3% of the population of boys at least 105 cm tall has a weight of 14.0 kg or less. In particular, at most 3% of the population of boys at least 105 cm tall has a weight of exactly 14.0 kg.

The correct answer is Yes.

Using Height-for-age standards, the 85th percentile in height for boys 5 years 0 months is 114.8 cm. This means that a boy 114.8 cm tall is as tall or taller than 85% of boys aged 5 years 0 months. It does not follow that a boy 114.8 cm tall is necessarily taller than 85% of boys aged 5 years 0 months, so it is not necessarily true of a boy 114 cm tall, either.

The correct answer is No.


2. Consider an individual boy from a model population. Suppose that from age 2 through age 5, this boy's weight is at the 97th percentile for his height and his height is at the 97th percentile for his age. Which one of the following statements must be true of the boy at age 5 years 0 months?

Neither Height-for-age standards nor Weight-for-height standards provide a distribution of age on the basis of weight, height, or any other variable, so it is impossible to determine where the boy's age falls in the distribution of age for height (choice A).

The boy's weight is less than that of 97% of boys his height, and his height is less than that of 97% of boys his age, but it is impossible to tell where his weight falls among the weights of boys his age (choice B).

Likewise, knowing height-for-weight percentiles does not provide information about weight-for-height percentiles (choice C).

However, it is possible to approximate his height at each age and his weight at each height; thus it is possible to determine his weight at each age. Height-for-age standards indicates that at age 2 years 0 months, the boy was 92.9 cm tall, and at age 5 years 0 months, he was 118.7 cm tall. Weight-for-height standards indicates that the 97th percentile weight for boys 92.9 cm tall is approximately 16 kg, while the 97th percentile weight for boys 118.7 cm tall is between 26 kg and 27 kg. Thus his weight at age 5 years 0 months is roughly between 26/16 = 162 .5% and 27/16 = 168 .75%, or approximately 166%, of his weight at age 2 years 0 months.

The correct answer is D.


3. B is a boy aged 4 years 3 months whose height is 110 cm and whose weight is 19 kg. For each of the following statements, select Yes if, based on the given information, it must be true of B relative to a model population. Otherwise, select No.

Neither Height-for-age standards nor Weight-for-height standards provide a distribution of height on the basis of weight, so it is impossible to determine the proportion of boys weighing 19 kg whose height is less than 110 cm.

The correct answer is No.

Using the table in Height-for-age standards, the 85th percentile in height for boys aged 4 years 3 months is 109.5 cm, so (100 − 85)%, or 15%, of boys aged 4 years 3 months are taller than 109.5 cm. Thus, at most 15% of boys of this age are taller than B's height of 110 cm.

The correct answer is Yes.

Using the table in Height-for-age standards, the 50th percentile in height for boys aged 5 years 0 months is 110.0 cm, which is the same height as B. Therefore, B's height is greater than or equal to that of (100 − 50)%, or 50%, of boys aged 5 years 0 months.

The correct answer is Yes.


4. B is a boy aged 4 years 3 months whose height is 110 cm and whose weight is 19 kg. For each of the following statements, select Yes if, based on the given information, it must be true of B relative to a model population. Otherwise, select No.

According to the graph in Weight-for-height standards, the 15th percentile in weight for a boy of height 110 cm is approximately 17 kg. Therefore, 17 kg is greater than or equal to the weight of 15% of boys of that height. But 17 kg is less than B's weight of 19 kg, so the percentage of boys whose weight is less than or equal to B's weight may be somewhat larger than 15%. Consequently, at least 15% of boys at B's height have a weight that is less than or equal to that of B.

The correct answer is Yes.

B's height is 110 cm, and 10% of 110 is equal to 11, so a boy is within 10% of B's height provided that he is between 99 cm and 121 cm tall. According to Height-for-age standards, for boys aged 4 years 3 months, 100.5 cm is the 15th percentile in height and 113.1 cm is the 97th percentile in height. Therefore, (97 − 15)%, or 82% of boys B's age have heights between 100.5 cm and 113.1 cm. Since 99 < 100.5 and 113.1 < 121, the heights of all these boys are within 10% of B's height, so at least 82%—and hence at least 80%—of boys B's age have heights within 10% of B's height.

The correct answer is Yes.

According to Height-for-age standards, for boys aged 4 years 0 months, the 97th percentile in height is 111.2 cm, so B's height of 110 cm is less than that of at least 3% of boys this age. If B's height were also less than that of at most 3% of boys this age, then 110 cm would have to be the 97th percentile in height for boys aged 4 years 0 months, which it is not.

The correct answer is No


5. For each of the following statements, select Yes if the statement must be true of a boy selected at random from a model population. Otherwise, select No.

Using Height-for-age standards for boys aged 4 years 0 months, the 15th percentile in height is 99.0 cm. Thus, 15% of boys of this age are 99.0 cm tall or shorter. Note that the 3rd percentile in height for boys of this age is 95.4 cm, so 3% of boys of this age are at this height or shorter. Therefore, (15 − 3)%, or 12% of boys aged 4 years 0 months have heights greater than 95.4 cm and less than or equal to 99.0 cm. The proportion of boys of this age whose height is exactly 99.0 cm must therefore be less than or equal to 12%, so the indicated probability is also less than or equal to 12%.

The correct answer is No.

Using Height-for-age standards, the 3rd percentile in height for ages from 2 years 0 months through 5 years 0 months is at least 81.4 cm. This means that a boy from a model population whose height is 81.4 cm is shorter than at least 97% of boys his age. Thus, a boy who is 81 cm tall is shorter than at least 97% of boys his age and thus shorter than at least 95% of boys his age.

The correct answer is Yes.

Weight-for-height standards provide a weight distribution for boys 120 cm tall; in particular, 97% of boys at this height weigh more than 18 kg. But a randomly selected boy at this height could conceivably weigh much less than 18 kg. Moreover, even if the boy's weight were known, a percentile distribution of weight for boys age 2 years 6 months is lacking, so it is impossible to answer the question based on the information provided.

The correct answer is No.


6. Consider an individual boy from a model population. Suppose that from age 2 through age 5, this boy’s weight is at the 50th percentile for his height and his height is at the 50th percentile for his age. Which one of the following statements must be true of the boy at age 5 years 0 months?

Neither Height-for-age standards nor Weight-for-height standards provide a distribution of age on the basis of weight, height, or any other variable, so it is impossible to determine where the boy's age falls in the distribution of age for height (option A). The boy's weight is less than that of 50% of boys his height, and his height is less than that of 50% of boys his age, but it is impossible to tell where his weight falls among the weights of boys his age (option B). Likewise, knowing height-for-weight percentiles does not provide information about weight-for-height percentiles (option C).

What can be approximated, however, is his height at each age and his weight at each height; thus, it is possible to know his weight at each age. Height-for-age standards indicates that at age 2 years 0 months, the boy was 87.1 cm tall, and at age 5 years 0 months, he was 110.0 cm tall. Weight-for-height standards indicates that the 50th percentile weight for boys 87.1 cm tall is approximately 12 kg, while the 50th percentile weight for boys 110.0 cm tall is approximately 18 kg. Thus, his weight at age 5 years 0 months is approximately 18/12 (100)%, or 150%, of his weight at age 2 years 0 months.

The correct answer is D.
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Re: The World Health Organization (WHO) has produced a comprehensive set o [#permalink] New post  16 Jul 2012, 04:33
1) yes ---> 3.3 --> 50th--> 98.0.

2) yes ---> at least 3rd ---> line black

3) no ----> at least 85% line green -----> no
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Re: The World Health Organization (WHO) has produced a comprehensive set o [#permalink] New post  16 Jul 2012, 07:19
carcass wrote:
1) yes ---> 3.3 --> 50th--> 98.0.

2) yes ---> at least 3rd ---> line black

3) no ----> at least 85% line green -----> no



the definition is as nth percentile in height for a given age is the unique height among boys of that age that is greater than or equal to n percent, and less than or equal to (100- n) percent

so for Q.A : how can you be sure that the probability is greater than 50%
it can be 50% as well, right?
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Re: The World Health Organization (WHO) has produced a comprehensive set o [#permalink] New post  16 Jul 2012, 09:13
your area where you are looking for your answer ;) > 3.3......so 3.6 and so on......
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Re: The World Health Organization (WHO) has produced a comprehensive set o [#permalink] New post  11 Feb 2017, 07:20
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For question 1 isn't this scenario possible
:Let age be 3.6 and 98cms correspond to 49 percentile.
because in the first graph Age 3.6 and height 99.9 corresponds to 50th percentile so isn't it also possible that 98cms may be in the 49th percentile.
Please see the attached table illustrating this scenario.
Can some expert please point out why in table 3.1 the scenario highlighted in Green in not possible?

In the table above I have just added two more percentiles 45th and 49th in between 15th and 50th, and two single month increments between ages 3.3 and 3.6. This extra data has been highlighted in Grey.
The table is consistent with the rest of the data given in the original table.
There is an increment in height as we go from left to right and also there is an increment in height as we go from top to bottom.

Question 1 states:
A. If his age is greater than 3 years 3 months; the probability that his height is at least 98.0 cm is greater than 50%.

if we look at the table then the scenario in green is a possibility is it not? The scenario in green states that, at age 3.6 if height is 98.0 then it is in the 49th percentile.

So height 98cms at age greater than 3.3 need not be greater than 50th percentile.

So if the scenario in the table above is possible then answer to question 1 need NOT be yes.
Can experts please tell why the scenario in Green in not possible?

Thank you.
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Re: The World Health Organization (WHO) has produced a comprehensive set o [#permalink] New post  02 Jan 2021, 15:52
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Bunuel Can you please help with Baybeam's questions? Thanks in advance!
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Re: The World Health Organization (WHO) has produced a comprehensive set o [#permalink] New post  15 Mar 2021, 05:25
Bloddy Helll!!! Can anyone please explain the prompt in simple english ????
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Re: The World Health Organization (WHO) has produced a comprehensive set o [#permalink] New post  29 Nov 2021, 17:07
Sajjad1994

Why did you skip #2?
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Re: The World Health Organization (WHO) has produced a comprehensive set o [#permalink] New post  30 Nov 2021, 01:27
Expert Reply
GK002 wrote:
Sajjad1994

Why did you skip #2?


Hi GK002

Unfortunately, I do not have the OE of question #2.

I have posted the OEs from the EA course and the course skipped question #2.
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Re: The World Health Organization (WHO) has produced a comprehensive set o [#permalink] New post  06 Dec 2021, 04:17
Can anyone post the answer for Question 2
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Re: The World Health Organization (WHO) has produced a comprehensive set o [#permalink] New post  20 Jul 2022, 20:30
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6. Consider an individual boy from a model population. Suppose that from age 2 through age 5, this boy’s weight is at the 50th percentile for his height and his height is at the 50th percentile for his age. Which one of the following statements must be true of the boy at age 5 years 0 months?

Neither Height-for-age standards nor Weight-for-height standards provide a distribution of age on the basis of weight, height, or any other variable, so it is impossible to determine where the boy's age falls in the distribution of age for height (option A).


Based on this explanation, the OA for Q2 CANNOT be A.

Q2 and Q6 are basically the same kind of questions. Here's OE for Q2:

Neither Height-for-age standards nor Weight-for-height standards provide a distribution of age on the basis of weight, height, or any other variable, so it is impossible to determine where the boy's age falls in the distribution of age for height (choice A).

The boy's weight is less than that of 97% of boys his height, and his height is less than that of 97% of boys his age, but it is impossible to tell where his weight falls among the weights of boys his age (choice B).

Likewise, knowing height-for-weight percentiles does not provide information about weight-for-height percentiles (choice C).

However, it is possible to approximate his height at each age and his weight at each height; thus it is possible to determine his weight at each age. Height-for-age standards indicates that at age 2 years 0 months, the boy was 92.9 cm tall, and at age 5 years 0 months, he was 118.7 cm tall. Weight-for-height standards indicates that the 97th percentile weight for boys 92.9 cm tall is approximately 16 kg, while the 97th percentile weight for boys 118.7 cm tall is between 26 kg and 27 kg. Thus his weight at age 5 years 0 months is roughly between 26/16 = 162 .5% and 27/16 = 168 .75%, or approximately 166%, of his weight at age 2 years 0 months.

The correct answer is D.
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Re: The World Health Organization (WHO) has produced a comprehensive set o [#permalink] New post  28 Jul 2023, 07:41
Sajjad1994 Can you please explain why Option B in Q2 is incorrect. The question states that the weight and the height are at 97 percentile, but the OE changes them to less than 97
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Re: The World Health Organization (WHO) has produced a comprehensive set o [#permalink] New post  06 Sep 2023, 14:11
Why are we unable to infer height based on weight using the weight-for-height graph? Does that graph not display height on the basis of weight and vice versa?
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Re: The World Health Organization (WHO) has produced a comprehensive set o [#permalink] New post  25 Dec 2023, 05:51
hi Sajjad1994 and other experts,

it its tough for me to understand this sentence
In a model population, for n = 3, 15, 50, 85, and 97, the nth percentile in weight for a given height is the unique weight among boys of that height that is greater than or equal to n percent, and less than or equal to (100 - n) percent, of weights of boys of that height.

would you please help clarify further?

thanks in advance
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Re: The World Health Organization (WHO) has produced a comprehensive set o [#permalink] New post  03 Mar 2024, 02:55
zoezhuyan wrote:
hi Sajjad1994 and other experts,

it its tough for me to understand this sentence
In a model population, for n = 3, 15, 50, 85, and 97, the nth percentile in weight for a given height is the unique weight among boys of that height that is greater than or equal to n percent, and less than or equal to (100 - n) percent, of weights of boys of that height.

would you please help clarify further?

thanks in advance

­Hi. This basically implies that if I say I am 97 percentile in weight, then 97 percent of people of my age will be equal to or less than my weight and 3 (100-97) percent of people of my age will have a weight greater than mine. They have basically tried to overcomplicate the definition of percentile.

If I say that my weight is 100 grams and it is 60 percentile. Then, 40 percent of people are heavier than 100 grams, while 60 percent people are 100 grams or less.
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