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Data can be “distributed” (spread out) in different ways.

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Normal Distribution Word Problems Examples

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On example of working a normal distribution word problems, involving a lower cut off point. I also use the z-formula and z-table.

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3. More examples of Normal distributions

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3. More examples of Normal distributions

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Stats 19   Z Score and Normal Distribution Examples

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In this video we solve several problems related to probabilities and the Normal Distribution. Includes solving for observed values, expected values, standard deviations, and cumulative probabilities.

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4. Determine your z-score for your height (how many standard deviations above or below the mean you are).  Go to this site to find out the average height for someone your age and gender, then calculate your z score.  You can check your answer, and then hit the calculate button to see if your calculations were accurate.  Do your calculations ahead of time, and tell me if your conclusion matched the website's conclusion.  Bring this in tomorrow for your homework! 

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4. Determine your z-score for your height (how many standard deviations above or below the mean you are).  Go to this site to find out the average height for someone your age and gender, then calculate your z score.  You can check your answer, and then hit the calculate button to see if your calculations were accurate.  Do your calculations ahead of time, and tell me if your conclusion matched the website's conclusion.  Bring this in tomorrow for your homework! 

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Below is a height percentile calculator. It works for all ages including newborns, babies, toddlers, children, teenagers, and adults right up to the elderly. Note though that you can only specify a country when 'Adult' is selected. If your country isn't listed, you can choose custom and enter your country's average height manually into the height percentile calculator.

This height percentile calculator is only for information purposes and is not for medical purposes. There are many reasons why the results may not be relevant for any given individual. For example, percentiles for outliers may be exaggerated. Also, ethnicity is not considered. Please see the discussion below for more information on height percentile calculators.

Percentiles are used in statistics to indicate the percentage of observations that fall in a group. In the case of height percentiles, the observation is height and the group is people that are shorter. So if someone has a height percentile of 75, then 75% of the relevant population is shorter. The other 25%, of course, is taller. Besides the above calculator, percentiles can also come from growth charts.

Percentiles are useful for many purposes including recognizing when an individual is exceptionally short or tall. This affords an opportunity to look for an underlying cause, which could be a height related disorder . Specialists that can help with this include endocrinologists, pediatricians, and geneticists. Percentiles are also an alternative to height calculators for predicting adult height as percentiles will generally remain similar into adulthood. However, it is important to note that the above height percentile calculator is based on statistical averaging and there are many reasons why it may not provide relevant data for an individual. For example, it does not take into account ethnicity. It also assumes a perfectly normal height distribution, whereas human height distribution merely approximates this. This leads to error particularly for extreme short or tall stature.

The above height percentile calculator has some extras compared to most others out there. For starters, it takes into account age. Age ranges include newborn, baby, toddler, child, teenager, and adults right up to the elderly. This is important as both average height and height distribution change with age.

The height percentile calculator can also factor in country. Included countries are the U.S., Canada, most European countries, and over one hundred in total. This is important as average height varies considerably from one country to the next. Unfortunately, age specific data for all these countries is hard to come by. Hence country selection is disabled for all age selections but 'Adult'.

All age specific data came from the Centers for Disease Control [1,2], except for ages 0 to 2, which came from the World Health Organization [3]. Note that height for ages 0 to 2 is actually measured as length.

The country specific data came from Wikipedia. For the U.S., these stats coincide with the most recent from the Centers for Disease Control [1]. Note that data for the entire adult age range was used when available. By including the elderly, average height is lowered. This is because people decrease in stature with age and older generations were shorter. If you want to calculate a height percentile for a more limited age range, you can enter other data you get from Wikipedia or elsewhere.

The height percentile calculator also lets you specify male or female gender. Some country specific data was missing one gender. To fill in the missing data, an average 8% gender height gap was used.

The population standard deviation is automatically set for you. Here, standard deviation is a measure of how spread out human height is. A larger standard deviation means a greater variation in height. The standard deviation automatically set in the height percentile calculator is approximated from Centers for Disease Control and World Health Organization data [1,2,3]. Specific countries will vary somewhat from this. If you want the most accurate height percentile assessment, you should find country specific standard deviation and enter that.

Based on this standard deviation, the height percentile calculator determines how many standard deviations (also called the standard score or Z-score) the individual's height is from average. This can then be used to determine percentile. For example, a standard deviation of 1 corresponds with the 84.2 nd percentile, 2 the 97.8 th, and 3 the 99.9 th. Note that as height becomes extreme, the percentile changes very little while the standard deviations from average changes linearly. Hence outliers may gain more insight from considering their standard deviations from average rather than their height percentile.

The height percentile calculator also uses the number of standard deviations from average to categorize height as in the below table. Height definitions are discussed more here: Defining Tall. Lastly, the height percentile calculator determines the number of people the individual would likely have to meet to find someone at least as short or as tall.

For more height related calculators, see here: calculator

SD < -3

Extremely Short

-3 < SD < -2

Short

-2 < SD < -1

Kinda Short

-1 < SD < 0

Below Average

SD = 0

Average

0 < SD < 1

Above Average

1 < SD < 2

Kinda Tall

2 < SD < 3

Tall

3 < SD

Extremely Tall

[1] Anthropometric Reference Data for Children and Adults: United States, 2007-2010
[2]CDC Percentile Data Files
[3]WHO Child Growth Standards

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Height Percentile Calculator, by Age or Country

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Below is a height percentile calculator. It works for all ages including newborns, babies, toddlers, children, teenagers, and adults right up to the elderly. Note though that you can only specify a country when 'Adult' is selected. If your country isn't listed, you can choose custom and enter your country's average height manually into the height percentile calculator.

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Tell me how your results in the activity in #4 match up to your self image?