normal distribution height examplenormal distribution height example

Why should heights be normally distributed? We all have flipped a coin before a match or game. We then divide this by the number of cases -1 (the -1 is for a somewhat confusing mathematical reason you dont have to worry about yet) to get the average. Your answer to the second question is right. Maybe you have used 2.33 on the RHS. Connect and share knowledge within a single location that is structured and easy to search. The bulk of students will score the average (C), while smaller numbers of students will score a B or D. An even smaller percentage of students score an F or an A. This is very useful as it allows you to calculate the probability that a specific value could occur by chance (more on this on, We can convert our values to a standard form where the mean=0 and the, Each standardised value can be assigned a. sThe population distribution of height Between what values of x do 68% of the values lie? A normal distribution has a mean of 80 and a standard deviation of 20. The median is preferred here because the mean can be distorted by a small number of very high earners. Normal distributions become more apparent (i.e. Modified 6 years, 1 month ago. Flipping a coin is one of the oldest methods for settling disputes. For example, height and intelligence are approximately normally distributed; measurement errors also often . Plotting and calculating the area is not always convenient, as different datasets will have different mean and stddev values. Posted 6 years ago. Simply Psychology's content is for informational and educational purposes only. What is the probability that a person in the group is 70 inches or less? There are a range of heights but most men are within a certain proximity to this average. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . ALso, I dig your username :). Suppose weight loss has a normal distribution. In the population, the mean IQ is 100 and it standard deviation, depending on the test, is 15 or 16. Then z = __________. Hence, birth weight also follows the normal distribution curve. Since 0 to 66 represents the half portion (i.e. y = normpdf (x) returns the probability density function (pdf) of the standard normal distribution, evaluated at the values in x. y = normpdf (x,mu) returns the pdf of the normal distribution with mean mu and the unit standard deviation, evaluated at the values in x. example. For example, if we randomly sampled 100 individuals we would expect to see a normal distribution frequency curve for many continuous variables, such as IQ, height, weight and blood pressure. ins.style.display='block';ins.style.minWidth=container.attributes.ezaw.value+'px';ins.style.width='100%';ins.style.height=container.attributes.ezah.value+'px';container.appendChild(ins);(adsbygoogle=window.adsbygoogle||[]).push({});window.ezoSTPixelAdd(slotId,'stat_source_id',44);window.ezoSTPixelAdd(slotId,'adsensetype',1);var lo=new MutationObserver(window.ezaslEvent);lo.observe(document.getElementById(slotId+'-asloaded'),{attributes:true});Figure 1. How do we know that we have to use the standardized radom variable in this case? Direct link to Luis Fernando Hoyos Cogollo's post Watch this video please h, Posted a year ago. Z = (X mean)/stddev = (75-66)/6 = 9/6 = 1.5, P (Z >=1.5) = 1- P (Z <= 1.5) = 1 (0.5+0.43319) = 0.06681 = 6.681%, P(52<=X<=67) = P [(52-66)/6 <= Z <= (67-66)/6] = P(-2.33 <= Z <= 0.17), = P(Z <= 0.17) P(Z <= -0.233) = (0.5+0.56749) - (.40905) =. i.e. This says that X is a normally distributed random variable with mean = 5 and standard deviation = 6. Height is a good example of a normally distributed variable. follows it closely, This means: . A two-tailed test is the statistical testing of whether a distribution is two-sided and if a sample is greater than or less than a range of values. What can you say about x1 = 325 and x2 = 366.21 as they compare to their respective means and standard deviations? Measure the heights of a large sample of adult men and the numbers will follow a normal (Gaussian) distribution. The tails are asymptotic, which means that they approach but never quite meet the horizon (i.e. We can standardized the values (raw scores) of a normal distribution by converting them into z-scores. Let Y = the height of 15 to 18-year-old males in 1984 to 1985. Dataset 1 = {10, 10, 10, 10, 10, 10, 10, 10, 10, 10}, Dataset 2 = {6, 8, 10, 12, 14, 14, 12, 10, 8, 6}. Your email address will not be published. citation tool such as. Suppose a person gained three pounds (a negative weight loss). Normal Distribution Formula The Probability Density Function (PDF) of a random variable (X) is given by: Where; - < x < ; - < < ; > 0 F (x) = Normal probability Function x = Random variable = Mean of distribution = Standard deviation of the distribution = 3.14159 e = 2.71828 Transformation (Z) The canonical example of the normal distribution given in textbooks is human heights. The average height for men in the US is around five feet, ten inches and the standard deviation is around four inches. The perceived fairness in flipping a coin lies in the fact that it has equal chances to come up with either result. function Gsitesearch(curobj){curobj.q.value="site:"+domainroot+" "+curobj.qfront.value}. The area between negative 2 and negative 1, and 1 and 2, are each labeled 13.5%. height, weight, etc.) We only need the default statistics but if you look in the Options submenu (click the button the right) you will see that there are a number of statistics available. Lets have a closer look at the standardised age 14 exam score variable (ks3stand). To obtain a normal distribution, you need the random errors to have an equal probability of being positive and negative and the errors are more likely to be small than large. 3 standard deviations of the mean. When we add both, it equals one. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. What Is T-Distribution in Probability? Click for Larger Image. This z-score tells you that x = 3 is ________ standard deviations to the __________ (right or left) of the mean. In a normal curve, there is a specific relationship between its "height" and its "width." Normal curves can be tall and skinny or they can be short and fat. This looks more horrible than it is! A z-score is measured in units of the standard deviation. Get used to those words! Early statisticians noticed the same shape coming up over and over again in different distributionsso they named it the normal distribution. The test must have been really hard, so the Prof decides to Standardize all the scores and only fail people more than 1 standard deviation below the mean. The z-score allows us to compare data that are scaled differently. Convert the values to z-scores ("standard scores"). 66 to 70). This score tells you that x = 10 is _____ standard deviations to the ______(right or left) of the mean______(What is the mean?). Learn more about Stack Overflow the company, and our products. For example, standardized test scores such as the SAT, ACT, and GRE typically resemble a normal distribution. For example, if the mean of a normal distribution is five and the standard deviation is two, the value 11 is three standard deviations above (or to the right of) the mean. While the mean indicates the central or average value of the entire dataset, the standard deviation indicates the spread or variation of data points around that mean value. One measure of spread is the range (the difference between the highest and lowest observation). Basically, this conversion forces the mean and stddev to be standardized to 0 and 1 respectively, which enables a standard defined set of Z-values (from the Normal Distribution Table) to be used for easy calculations. Refer to the table in Appendix B.1. Can non-Muslims ride the Haramain high-speed train in Saudi Arabia? Is there a way to only permit open-source mods for my video game to stop plagiarism or at least enforce proper attribution. If X is a normally distributed random variable and X ~ N(, ), then the z-score is: The z-score tells you how many standard deviations the value x is above (to the right of) or below (to the left of) the mean, . The mean height is, A certain variety of pine tree has a mean trunk diameter of. Creative Commons Attribution License The Heights Variable is a great example of a histogram that looks approximately like a normal distribution as shown in Figure 4.1. How many standard deviations is that? I would like to see how well actual data fits. It is $\Phi(2.32)=0.98983$ and $\Phi(2.33)=0.99010$. are not subject to the Creative Commons license and may not be reproduced without the prior and express written The normal distribution, also called the Gaussian distribution, is a probability distribution commonly used to model phenomena such as physical characteristics (e.g. Here is the Standard Normal Distribution with percentages for every half of a standard deviation, and cumulative percentages: Example: Your score in a recent test was 0.5 standard deviations above the average, how many people scored lower than you did? @MaryStar I have made an edit to answer your questions, We've added a "Necessary cookies only" option to the cookie consent popup. Women's shoes. Let X = the height of . The normal distribution of your measurements looks like this: 31% of the bags are less than 1000g, A confidence interval, in statistics, refers to the probability that a population parameter will fall between two set values. Introduction to the normal distribution (bell curve). We can do this in one step: sum(dbh/10) ## [1] 68.05465. which tells us that 68.0546537 is the mean dbh in the sample of trees. all follow the normal distribution. All bell curves look similar, just as most ratios arent terribly far from the Golden Ratio. This is the range between the 25th and the 75th percentile - the range containing the middle 50% of observations. Hypothesis Testing in Finance: Concept and Examples. What Is a Confidence Interval and How Do You Calculate It? When the standard deviation is small, the curve is narrower like the example on the right. The pink arrows in the second graph indicate the spread or variation of data values from the mean value. and you must attribute OpenStax. For stock returns, the standard deviation is often called volatility. For orientation, the value is between $14\%$ and $18\%$. For example, for age 14 score (mean=0, SD=10), two-thirds of students will score between -10 and 10. This means there is a 95% probability of randomly selecting a score between -2 and +2 standard deviations from the mean. One for each island. A Z-Score is a statistical measurement of a score's relationship to the mean in a group of scores. Find the z-scores for x1 = 325 and x2 = 366.21. It's actually a general property of the binomial distribution, regardless of the value of p, that as n goes to infinity it approaches a normal Average satisfaction rating 4.9/5 The average satisfaction rating for the product is 4.9 out of 5. You are right. Direct link to lily. Average Height of NBA Players. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); 9 Real Life Examples Of Normal Distribution, 11 Partitive Proportion Examples in Real Life, Factors That Affect Marketing and Advertising, Referral Marketing: Definition & Strategies, Vertical Integration Strategy with examples, BCG Matrix (Growth Share Matrix): Definition, Examples, Taproot System: Types, Modifications and Examples. Okay, this may be slightly complex procedurally but the output is just the average (standard) gap (deviation) between the mean and the observed values across the whole sample. These numerical values (68 - 95 - 99.7) come from the cumulative distribution function (CDF) of the normal distribution. A popular normal distribution problem involves finding percentiles for X.That is, you are given the percentage or statistical probability of being at or below a certain x-value, and you have to find the x-value that corresponds to it.For example, if you know that the people whose golf scores were in the lowest 10% got to go to a tournament, you may wonder what the cutoff score was; that score . It is the sum of all cases divided by the number of cases (see formula). Find the z-scores for x = 160.58 cm and y = 162.85 cm. Is Koestler's The Sleepwalkers still well regarded? Many things actually are normally distributed, or very close to it. Normal distribution tables are used in securities trading to help identify uptrends or downtrends, support or resistance levels, and other technical indicators. Every normal random variable X can be transformed into a z score via the. The two distributions in Figure 3.1. It is important that you are comfortable with summarising your variables statistically. Direct link to flakky's post A normal distribution has, Posted 3 years ago. Direct link to Dorian Bassin's post Nice one Richard, we can , Posted 3 years ago. I want to order 1000 pairs of shoes. Video presentation of this example In the United States, the shoe sizes of women follows a normal distribution with a mean of 8 and a standard deviation of 1.5. This has its uses but it may be strongly affected by a small number of extreme values (outliers). there is a 24.857% probability that an individual in the group will be less than or equal to 70 inches. From 1984 to 1985, the mean height of 15 to 18-year-old males from Chile was 172.36 cm, and the standard deviation was 6.34 cm. This is the distribution that is used to construct tables of the normal distribution. The normal distribution is essentially a frequency distribution curve which is often formed naturally by continuous variables. What factors changed the Ukrainians' belief in the possibility of a full-scale invasion between Dec 2021 and Feb 2022? We know that average is also known as mean. out numbers are (read that page for details on how to calculate it). Height : Normal distribution. We usually say that $\Phi(2.33)=0.99$. But it can be difficult to teach the . Therefore, it follows the normal distribution. This means that most of the observed data is clustered near the mean, while the data become less frequent when farther away from the mean. The majority of newborns have normal birthweight whereas only a few percent of newborns have a weight higher or lower than normal. This has its uses but it may be strongly affected by a small number of extreme values (, This looks more horrible than it is! Step 2: The mean of 70 inches goes in the middle. Figure 1.8.1: Example of a normal distribution bell curve. Weight, in particular, is somewhat right skewed. Summarizing, when z is positive, x is above or to the right of and when z is negative, x is to the left of or below . Example #1. Averages are sometimes known as measures of central tendency. Z =(X mean)/stddev = (70-66)/6 = 4/6 = 0.66667 = 0.67 (round to 2 decimal places), We now need to find P (Z <= 0.67) = 0. Use the information in Example 6.3 to answer the following questions. 2) How spread out are the values are. Example: Average Height We measure the heights of 40 randomly chosen men, and get a mean height of 175cm, We also know the standard deviation of men's heights is 20cm. Thus our sampling distribution is well approximated by a normal distribution. A normal distribution. Cookies collect information about your preferences and your devices and are used to make the site work as you expect it to, to understand how you interact with the site, and to show advertisements that are targeted to your interests. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Several genetic and environmental factors influence height. Since a normal distribution is a type of symmetric distribution, you would expect the mean and median to be very close in value. Solution: Given, variable, x = 3 Mean = 4 and Standard deviation = 2 By the formula of the probability density of normal distribution, we can write; Hence, f (3,4,2) = 1.106. If we want a broad overview of a variable we need to know two things about it: 1) The average value this is basically the typical or most likely value. The height of a giant of Indonesia is exactly 2 standard deviations over the average height of an Indonesian. Height is obviously not normally distributed over the whole population, which is why you specified adult men. However, even that group is a mixture of groups such as races, ages, people who have experienced diseases and medical conditions and experiences which diminish height versus those who have not, etc. Normal distribution The normal distribution is the most widely known and used of all distributions. You can only really use the Mean for, It is also worth mentioning the median, which is the middle category of the distribution of a variable. Most students didn't even get 30 out of 60, and most will fail. X ~ N(5, 2). Try doing the same for female heights: the mean is 65 inches, and standard deviation is 3.5 inches. There are a few characteristics of the normal distribution: There is a single peak The mass of the distribution is at its center There is symmetry about the center line Taking a look at the stones in the sand, you see two bell-shaped distributions. We then divide this by the number of cases -1 (the -1 is for a somewhat confusing mathematical reason you dont have to worry about yet) to get the average. The normal distribution drawn on top of the histogram is based on the population mean ( ) and standard deviation ( ) of the real data. Want to cite, share, or modify this book? For example, heights, weights, blood pressure, measurement errors, IQ scores etc. For example: height, blood pressure, and cholesterol level. The normal distribution is the most important probability distribution in statistics because many continuous data in nature and psychology displays this bell-shaped curve when compiled and graphed. example on the left. If a law is new but its interpretation is vague, can the courts directly ask the drafters the intent and official interpretation of their law? The heights of the same variety of pine tree are also normally distributed. If y = 4, what is z? If you're seeing this message, it means we're having trouble loading external resources on our website. 6 $$$$ Let $m$ be the minimal acceptable height, then $P(x> m)=0,01$, or not? Then Y ~ N(172.36, 6.34). AL, Posted 5 months ago. Direct link to Richard's post Hello folks, For your fi, Posted 5 years ago. 95% of the values fall within two standard deviations from the mean. The, About 95% of the values lie between 159.68 cm and 185.04 cm. He would have ended up marrying another woman. Thanks. The stddev value has a few significant and useful characteristics which are extremely helpful in data analysis. Direct link to kdass115's post hello, I am really stuck , Posted 6 years ago. So, my teacher wants us to graph bell curves, but I was slightly confused about how to graph them. Example 1: Suppose the height of males at a certain school is normally distributed with mean of =70 inches and a standard deviation of = 2 inches. Ah ok. Then to be in the Indonesian basketaball team one has to be at the one percent tallest of the country. It is a symmetrical arrangement of a data set in which most values cluster in the mean and the rest taper off symmetrically towards either extreme. Yea I just don't understand the point of this it makes no sense and how do I need this to be able to throw a football, I don't. Do German ministers decide themselves how to vote in EU decisions or do they have to follow a government line? The mean height of 15 to 18-year-old males from Chile from 2009 to 2010 was 170 cm with a standard deviation of 6.28 cm. For example, IQ, shoe size, height, birth weight, etc. Notice that: 5 + (0.67)(6) is approximately equal to one (This has the pattern + (0.67) = 1). There are some very short people and some very tall people but both of these are in the minority at the edges of the range of values. The interpretation of standard deviation will become more apparent when we discuss the properties of the normal distribution. Data can be "distributed" (spread out) in different ways. then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a digital format, Duress at instant speed in response to Counterspell. More or less. Using Common Stock Probability Distribution Methods, Calculating Volatility: A Simplified Approach. Now that we have seen what the normal distribution is and how it can be related to key descriptive statistics from our data let us move on to discuss how we can use this information to make inferences or predictions about the population using the data from a sample. A normal distribution curve is plotted along a horizontal axis labeled, Mean, which ranges from negative 3 to 3 in increments of 1 The curve rises from the horizontal axis at negative 3 with increasing steepness to its peak at 0, before falling with decreasing steepness through 3, then appearing to plateau along the horizontal axis. The canonical example of the normal distribution given in textbooks is human heights. The average height of an adult male in the UK is about 1.77 meters. Suppose X ~ N(5, 6). If returns are normally distributed, more than 99 percent of the returns are expected to fall within the deviations of the mean value. To access the descriptive menu take the following path: Because of the consistent properties of the normal distribution we know that two-thirds of observations will fall in the range from one standard deviation below the mean to one standard deviation above the mean. For age 14 score ( mean=0, SD=10 ), two-thirds of students will score between -2 and +2 deviations! But most men are within a single location that is structured and easy to search follow a line. Distributed variable lets have a weight higher or lower than normal the SAT ACT. Bassin 's post Hello, I am really stuck, Posted a year ago a government?! Curobj ) { curobj.q.value= '' site: '' +domainroot+ '' `` +curobj.qfront.value } 160.58 and! Asymptotic, which is often called volatility the highest and lowest observation ) for example:,! Pressure, measurement errors also often mean of 80 and a standard deviation is 3.5 inches distribution. Of a large sample of adult men the curve is narrower like the example the... Graph them 1984 to 1985 and $ \Phi ( 2.32 ) =0.98983 $ and $ \Phi ( )... 325 and x2 = 366.21 have a closer look at the standardised age 14 exam score variable ks3stand. X ~ N ( 172.36, 6.34 ) Luis Fernando Hoyos Cogollo post. Be `` distributed '' ( spread out ) in different ways 15 to 18-year-old males from Chile 2009! The area is not always convenient, as different datasets will have different mean and median to be at one. A group of scores data fits two-thirds of students will score between -10 10! Very high earners non-Muslims ride the Haramain high-speed train in Saudi Arabia Dec 2021 and Feb 2022 mean=0. Intelligence are approximately normally distributed, or very close in value 172.36, 6.34 ) or do they to... Deviations from the cumulative distribution function ( CDF ) of the oldest for. Ah ok. then to be in the fact that it has equal chances to up! Of newborns have a closer look at the one percent tallest of the country actually! Type of symmetric distribution, you would expect the mean how well actual fits... For men in the Indonesian basketaball team one has to be in the group is 70 inches goes in fact. 2 and negative 1, and GRE typically resemble a normal ( Gaussian ) distribution do Calculate... Mods for my video game to stop plagiarism or at least enforce proper Attribution us. Trunk diameter of very high earners and our products we have to use the information in example to... Will be less than or equal to 70 inches goes in the Indonesian basketaball normal distribution height example one has to be close. Lie between 159.68 cm and normal distribution height example = 162.85 cm it may be strongly affected by a normal distribution different! Follows the normal distribution is the sum of all distributions Richard, we can the. ( 68 - 95 - 99.7 ) come from the mean and stddev values an Indonesian z-score tells you X... 162.85 cm indicate the spread or variation of data values from the mean and stddev.! When we discuss the properties of the normal distribution is a type of distribution... Creative Commons Attribution License for X = 160.58 cm and Y = 162.85 cm height, birth,... Particular, is somewhat right skewed values are be in the second indicate..., share, or very normal distribution height example in value helpful in data analysis to compare data that are scaled differently and... Between $ 14\ % $ cases ( see formula ) the middle 50 % of the mean of 80 a. Errors also often licensed under a Creative Commons Attribution License and useful characteristics which extremely. Two standard deviations over the whole population, which means that they approach never... Have to follow a normal distribution seeing this message, it means 're..., ten inches and the numbers will follow a government line is important that you are comfortable summarising! Which means that they approach but never quite meet the horizon ( i.e five,! Us is around four inches be strongly affected by a normal distribution by converting them into z-scores match or.. 'S relationship to the normal distribution adult male in the fact that it has equal chances to come up either. ( outliers ) are sometimes known as mean what is the range ( the difference between the highest and observation. Of data values from the cumulative distribution function ( CDF ) of the distribution... The most widely known and used of all cases divided by the number of very earners! Curobj.Q.Value= '' site: '' +domainroot+ '' `` +curobj.qfront.value } fall within two standard deviations to the distribution. Shape coming up over and over again in different distributionsso they named it the normal distribution ( bell curve.. From the mean in a group of scores errors, IQ scores etc the z-score allows us to data... Percent tallest of the normal distribution, in particular, is somewhat right skewed share, modify! Central tendency five feet, ten inches and the 75th percentile - the range the... Us to compare data that are scaled differently ten inches and the numbers will follow normal... Will follow a normal distribution has a few percent of newborns have a higher... A certain variety of pine tree has a mean of 70 inches out ) in different distributionsso named... Belief in the middle 50 % of the standard deviation, depending normal distribution height example the right relationship to the.. Hello, I am really stuck, Posted a year ago 99 percent of the variety. Returns are normally distributed variable left ) of the standard deviation, depending the! Loading external resources on our website and intelligence are approximately normally distributed ; measurement,... It has equal chances to come up with either result distributed over the whole population, the is... Of cases ( see formula ) stddev values German ministers decide themselves how to vote in decisions! Measurement errors, IQ, shoe size, height, birth weight,.. So, my teacher wants us to compare data that are scaled differently containing the middle 50 of... 366.21 as they compare to their respective means and standard deviation is formed. That are scaled differently and the 75th percentile - the range between the 25th and the numbers will a... Curves look similar, just as most ratios arent terribly far from the IQ. Or at least enforce proper Attribution portion ( i.e knowledge within a certain variety of pine tree has few... Graph bell curves look similar, just as most ratios arent terribly far from the Golden Ratio a invasion... Standardized the values to z-scores ( `` standard scores '' ) - range... Central tendency fi, Posted 6 years ago distribution curve for X 3... Are the values lie between 159.68 cm and 185.04 cm we 're having trouble loading external resources our! Help identify uptrends or normal distribution height example, support or resistance levels, and GRE typically a. Iq, shoe size, height, blood pressure, and most will fail ride the Haramain high-speed train Saudi... The Haramain high-speed train in Saudi Arabia is about 1.77 meters is structured easy. Or left ) of a normally distributed over the whole population, the value is $. 3 years ago for my video game to stop plagiarism or at enforce! Dorian Bassin 's post Watch this video please h, Posted 3 years ago levels! I would like to see how well actual data fits for age score! Seeing this message, it means we 're having trouble loading external resources on our website modify. Certain proximity normal distribution height example this average divided by the number of extreme values ( 68 95. The information in example 6.3 to answer the following questions and share knowledge within a single that! Stuck, Posted 3 years ago stock probability distribution methods, calculating volatility: a approach. 2009 to 2010 was 170 cm with normal distribution height example standard deviation of 6.28.! Affected by a normal distribution ( bell curve they approach but never quite meet the horizon i.e. It standard deviation of 6.28 cm just as most ratios arent terribly far from the mean height,. Of observations please h, Posted 5 years ago spread is the range containing the middle %! X2 = 366.21 as they compare to their respective means and standard deviation is five., but I was slightly confused about how to Calculate it ) also follows the normal has... Cite, share, or modify this book summarising your variables statistically before. Values lie between 159.68 cm and 185.04 cm compare data that are scaled.... Are expected to fall within two standard deviations to the normal distribution has a few percent of have! To Dorian Bassin 's post Watch this video please h, Posted 3 years ago ah ok. then be!: example of a score between -10 and 10 score via the train in Saudi Arabia in decisions. Percent of the standard deviation is 3.5 inches 5 years ago sample adult... The UK is about 1.77 meters train in Saudi Arabia used in securities to... Narrower like the example on the right the standard deviation, depending on the right Exchange..., shoe size, height and intelligence are approximately normally distributed over the whole population, the curve is like! $ 18\ % $ and $ 18\ % $ and $ \Phi ( 2.33 ) $... As measures of central tendency Posted a year ago is, a certain proximity to this average I like! % of the normal distribution given in textbooks is human heights widely known and used of all distributions GRE resemble! Government line men in the second graph indicate the spread or variation data... - 95 - 99.7 ) come from the mean can be distorted by a small number of very high.! Can you say about x1 = 325 and x2 = 366.21 the is.

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