This is the penny data distribution by age from another class. The units represent age in years.
1. The photo shows the sampling distribution. Describe the distribution.
2. Did you comment on the penny on the shelf when describing the distribution? Is it unusual?
3. What was the nickel used to represent? Does it belong here?
3. Unfortunately only 14 students placed their mean age of a sample of 25 pennies. But what do you notice? (I replaced the quarters with blue chips in the second photo. It's the same data. )
6. Please look at the additional photos below to summarize how this data relates to the Central Limit Theorem and Sampling Distributions. Refer to the data. Use 9-B page 520 and others' posts if you have any other questions.
1. It's pretty symmetrically mound shaped, except for two low peaks in the middle. There are some outliers on the right side, but its hard to tell from the picture if they made the overall shape skewed. Center around 22cms
ReplyDelete2. Yes, it is a bit unusual, as it is an outlier that has a lower probability of occurring.
3. I'm not sure what the nickel means, maybe just 5 pennies?
4. There's a good amount of data around 25 pennies.
5. The more data there is in a sample, the closer the center will be to the population center. In this case, there wasn't quite enough data to get the center to the population center.
1. The distribution is somewhat mound shaped. The range is about 65 years. The mode is at 22 years. There is a possible outlier off the graph on the shelf.
ReplyDelete2. The penny on the shelf is unusual in its location but it is near other pennies according to year so it may not be an outlier.
3. The nickel was used to represent means of n=5 but the graph is for means of n=10.
4. The spread became much smaller with a sample size of 25 pennies. This shows less sampling variability with a larger n. The spread became 25 years instead of 65 years.
5. The Central Limit Theorem states that the frequency plot of the means of random samples will approximate a normal distribution as n increases. For this lab, when sample sizes of 10 and 25 were taken then averaged, the graph became increasingly more normal with a smaller standard deviation. Sampling distributions decrease as the sample size increases. The range of the sample size n=10 was 25 years and the range for n=25 was 9 years.
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ReplyDelete1. The graph is slightly mound shaped. It is a little bit skewed to the right and has a peak at approximately 22 years. The spread is approximately 57 years. The center is approximately 28 years. There are some possible outliers between around 53-57 years. There is one penny almost completely separated from the rest, on the shelf. Overall, the data seems to appear somewhat normally distributed.
ReplyDelete2. Yes, I did comment on the penny on the shelf. It is unusual which is why I described it as a possible outlier.
3. The nickel was used to represent the mean ages for sample sizes of 5. It does not belong here because this histogram is made with dimes to represent sample sizes of 10.
4. I notice that the peak is at 24 years, so with a sample size of 25, the mean age of the pennies is most frequently 24 years. I also noticed that the spread is very small, at about 9 years, meaning that the average mean of the ages of the pennies is very similar with each student's experiment. I also noticed that as the sample size increased, (from 1 to 5 to 10 to 25), the distribution got closer and closer to a normal distribution.
5. After observing the data and the different graphs closely, it is clear that the distribution is close to normal, and gets closer to normal with every increase in sample size. The graphs each make a mound shaped bell curve with somewhat symmetrical sides, thus appearing as normal. You can tell when n increases by the coin that it is represented by. It appears somewhat normal when n=1 (pennies), then appears even more normal when n=5 (nickels), and more normal for every other increase in size (n=10 is represented by dimes and n=25 is represented by quarters). This observation tells us that we are dealing with the central limit theorem. The central limit theorem states that as long as a population has a finite standard deviation, when n is large, the sampling distribution of the sample mean is close to the normal distribution. This explains why our distribution appears more normal when n increases.
1. The distribution is mostly mound shaped and has a possible high outlier, skewing it slightly to the right. The mode is at 22 years, and the center is also around there.
ReplyDelete2. Yes, I described it as a possible outlier. If it is an outlier, then it would be unusual, but there is other data close to it, so it may not be.
3. The nickel was used to represent the sampling distribution of means n=5, and it doesn't belong because dimes were used because n=10.
4. The spread of data decreased by about 40 years when the sample size decreased to 25. Also, the data is skewed to the left more and there is less variability.
5. The theorem states that the more data points, or as n increases, the more normal the distribution will be. We see this in the experiment where in the first part with many students participating, the graph was more mound shaped and closer to being normal. In the second section, where it was a distribution of only 14 students, there was a lot less variability and didn't follow the characteristics of a normal distribution as much as it would have with more data points.
1) shape: somewhat mound shaped, somewhat skewed right spread: 65 years center: about 22 possible outlier: on the shelf all the way to the right
ReplyDelete2) Yes, a possible outlier very unusual because it is set apart but not too far so it is still debatable whether it is an outlier or not.
3) The nickel was used to represent the sampling distribution of the mean ages for the sample size of n=5, this does not belong here because the graph is meant for means of n=10.
4) I noticed that the spread became smaller by about 40 years and the sample size decreased to 25. When there is a smaller sampling variability there is a larger spread.
5) As the sample sizes increase the graphs become more and more normal- this is true to the central limit theorem which states that if n is large the sampling distribution of the sample mean will be close to a normal distribution. The graph becomes more normal as the value of the coin increases ending with n=25 and a range of 9.
1. The graph is mound-shaped, but not symmetrical or uniform at all. It is skewed to the right, with a mode of 22 years. The center is approximately 20 years, the spread is about 56 years, and one possible outlier (the penny on the shelf).
ReplyDelete2. Yes, I said that the penny on the shelf is a possible outlier. Therefore this penny is unusual, especially if it actually is an outlier according to the outlier equation.
3. The nickel was used to represent the means for samples of 5 pennies. The nickel does not belong here because the dime graph is supposed to show means for samples of 10 pennies.
4. The mean of this histogram is 22.14 years. The graph is also skewed to the left rather than the right, and has a spread of 9 years, which means that the students' individual means were numerically similar. The graph also has less variability; as the sample size grew larger, the variability was reduced. The mode was 24, which is only slightly larger than the mode I estimated in question 1.
5. The central limit theorem states that for large n values, the sampling distribution of x̄ is approximately normal for any population with finite standard deviation σ. Essentially, as the sample size increases, the distribution will appear more normal. We see this in the above graphs; with the pennies (n=1), the graph seemed slightly normal, with the nickels (n=5), the graph seemed a little more normal, with the dimes (n=10), the graph seemed very normal, and with the quarters (n=25), the graph seemed the most normal. The central limit theorem supports the observations of increasing sample size accompanied by increasing normalcy.
1.)The shape of the graph is pretty mound shaped. It has a mode of 22. The range is somewhere around 60 to 65 years. There is a possible outlier all the way on the right side of the graph.
ReplyDelete2.) Yes I commented on the penny on the shelf. It could possibly be considered an outlier and in some cases maybe not. It is far away from the majority of the pennies but there still are a few near it. But also, we do not have an actual age for this penny, and maybe the person ran out of room and it is just the farthest away they could get, so there is some unknown information that could help.
3.) The nickel is used to represent a sample size of 5 pennies. It does not belong here because it is asking for the means of sampling distributions for 10 pennies.
4.) The spread has decreased greatly. This is because there is a very high n, which means there is a lot less variability. Compared to before when there was a very low n which resulted in high variability.
5.) The central limit theorem states that with a large n for a sample, the more likely it is to be a normal distribution. For the quarter or n=25, this should be pretty close to normal distribution, but like you said, unfortunately only 14 students plotted their points, so it was not the greatest representation.
1. The graph is somewhat mound-shaped, but not very uniform. It is skewed to the right with an approximate center of 30. There are several pennies that float off of the right side of the scale.
ReplyDelete2. Yes- it doesn't seem too unusual, just that the scale ran out and it didn't seem to require another ruler.
3. The nickel likely represent 5 or ten pennies. It doesn't belong in a graph where units are otherwise uniform.
4. There's a good amount of data in the second test, and the spread has been decreased.
5. The central limit theorem states that the larger n becomes in a sample, the more likely it is to be a normal distribution. When n = 25, the graph became significantly more normal.
1. The graph is mound shaped, with a mode of 22, and a spread of about 60. There are a few outlying pennies on the right side of the graph, specifically the one on the shelf.
ReplyDelete2. Yes, because it is the farthest point away from the rest of the data, making it unusual and a possible outlier.
3. The nickel was used to represent samples where n=5 (because a nickel is 5 cents), and does not belong one this graph because it is supposed to represent means of samples where n=10 (because a dime is 10 cents).
4. The spread and the variability decreased when the means of samples where n=25 are graphed. The spread is now about 25, and it is slightly skewed left.
5. The Central Limit Theorem (CLT) states that when the n of a sample becomes larger, the distribution is more likely to be normal. When n=25, the distribution became more normal.
1. The distribution of the graph is mound-shaped but skewed right. The center looks like 30. There could be a possible outlier (the penny on the shelve).
ReplyDelete2. Yes but I'm not sure it's necessarily an outlier because it's on the shelf.
3. The nickel and dime probably represent 5 and 10 pennies. It changes the shape of the graph.
4. The spread has been decreased.
5. The Central Limit Theory states that the larger the n, the more likely the distribution is normal. 25 data points is a pretty large number.
1. The graph is pretty mound-shaped, and seems skewed to the right. The range is about 65 years, the mode is about 22 years, and the center is around 25 years. There are some outliers around 55 years.
ReplyDelete2. Yes, it is unusual and a potential outlier.
3. The nickel represents 5 pennies. It does not belong there because the graph asks for distributions of 10 pennies.
4. The spread of the data decreased by about 40 years, and the center is around 25 years. There's a high n, so there's less variablility.
5. The central limit theorem states that if the sample has a large n, it is likely to be a normal distribution. When n is equal to 25, the graph becomes much more normal.
1.) The graph appears to be somewhat mound shaped but is not very uniform. The range is 60 to 65 and the mode is 22. The only possible outlier is all the way to the right.
ReplyDelete2.) Yes, I commented on the penny on the shelf. The penny could be seen as an outlier. It is distant from most of the pennies but there still are some surrounding it. There are many reasons why that penny would be there though.
3.) The nickel most likely represents 5 pennies. It doesn't belong here because the dime graph is supposed show the mean of 10 pennies.
4.) The spread has decreased in the second test. There is less variability.
5.) the central limit theorem states that the larger n is in a sample then the more likely the distribution will be normal. When n=25 the distribution will be closer to normal but only 14 students plotted points so it was not greatly represented
1) The graph is mound shaped but is not uniform and has a range is 60 to 65 and the mode is 22. The only possible outlier is all the way to the right.
ReplyDelete2.) The penny could be seen as an outlier.
3.) The nickel might represents 5 pennies. It doesn't belong here because the dime graph is supposed show the mean of 10 pennies.
4.) The spread has decreased in the second test. There is less variability.
5.) The central limit theorem says that the larger n is in a sample then the more likely the distribution will be normal. When n=25 the distribution will be closer to normal.
1. The Distribution is mound shaped. With a wide range and many data points. The center seems to be around 22. There is a tiny skew to the right. It is somewhat symmetrical.
ReplyDelete2. I didn't comment on the penny on the shelf but it is unusual. That number is probably an outlier or a number that cannot be on the number line.
3. The nickel may be an n of 5. It does not belong there because it just makes it more confusing.
4. I noticed that the numbers are very spread apart and the spread has decreased. They are not around 25 but all seem to be within a range of plus or minus ten.
5. There wasn't enough data to make the n = 25. This means that the sample was not large enough to be normal.
1.) The graph is mound shaped. Although, it seems to be bimodal. It is skewed right and the range is 60 to 65 and the mode is 22. There is one possible outlier all the way to the right.
ReplyDelete2.) Yes, I noticed and commented on the penny on the shelf. The penny could be an outlier when tested.
3.) The nickel most likely represents 5 pennies. It doesn't belong here because the dime graph is supposed to show the mean of 10 pennies.
4.) The spread has decreased in the second test. There is less variability.
5.) The central limit theorem states that the larger n is a sample then the more likely the distribution will be normal. When n=25 the distribution will be closer to normal but only 14 students plotted points so it was not greatly represented.
1. The distribution is skewed to the right, mound shaped, not uniform, the center is at about 30, and the spread is about 60.
ReplyDelete2. The penny is unusual because it is possibly an outlier.
3. The nickel represents n= 5 because it is equal to 5 pennies. It doesn't belong because it is supposed to show n=10, which are dimes not nickels.
4. The spread of the data and variability has decreased. The spread is about 25 now.
5. The central limit theorem says that if the sample has a large n, the more likely it will have a normal distribution. For n= 25, the distribution will be pretty normal. Although, only 14 students recorded their points so the distribution is not represented as well as it could be.
1. The mound-shaped distribution is skewed to the right, with a mode of about 22 and a range of 60 to 65.
ReplyDelete2. No, I did not. However, it is unusual because it could be an outlier.
3. The nickel probably represents 5 pennies, which is odd because the dime graph is supposed to show the mean of 10 pennies.
4. The spread and variability have decreased.
5. The sample was not nearly large enough to be "normal."
1. The distribution is skewed to the right, somewhat mound shape, range is 65 years, the mode is 22 years and there could be a possible outlier all the way to the end on the right on the shelf.
ReplyDelete2. Yes I commented on the penny on the shelf because even though it is far away from the other pennies it is still considered part of the graph. It could represent an outlier because all the pennies are on the board but this one is on the shelf.
3. The nickel was suppose to represent n=5 but it does not fit into the lab because the lab is n=10.
4. The spread went form 25 years to 65 years. With 25 pennies the spread and the data of variability became much smaller.
5. The Central Limit Theorem states that the means of a random sample will show a normal distribution as n increases. Sampling distributions decrease as the same size increases. Overall, the distribution will be relatively normal, but considering only 14 students recorded their years the distribution is not extremely well represented.
1. The graph is centered around 25, there are no visible outliers, is not uniform, is mound shaped, is skewed right, and has a spread of about 60.
ReplyDelete2. I didn't notice the penny, but now that it is pointed out it could be an outlier
3. The nickel probably means n=5, and it doesn't belong in the graph because we are discussing n=10 (dimes).
4. The spread and variability have both decreased.
5. The theorem states that as the n of a sample increases, it will become more normal. When n=14 the distribution isn't accurately represented, but when n=25, its much better.
1. The distribution of the graph shows a pretty mound shape, with a mode of 22 and a range at least above 52 years, I would say it is approximately around 65 years. There is also an outlier all the way to the right of the graph (the penny on the shelf).
ReplyDelete2. I commented on the penny on the shelf because I believe it is somewhat unusual and could be considered a potential outlier. There are some pennies near it however they don't have high frequencies and the majority of the pennies are farther to the left.
3. The nickel is used to represent a sample size of means n = 5 pennies. It does not belong however because the graph is for a sampling distribution with means of n = 10 pennies.
4. With a sample size of only 25 pennies the spread was reduced greatly to about 40 years. Prior to using 25 pennies there was high variability because the value of n was much smaller. However when we increase n we are reducing the variability. Larger samples sizes yield less variability.
5. According to the Central Limit Theorem (CLT) when a sample has a larger n then it is more likely to be a normal distribution than if the sample had a smaller n value. Therefore, when n = 25 it is more likely to have a normal distribution than if it were only n = 5 or 10 for example. However, because only 14 students plotted points (pennies) on the graph it isn't represented accurately.
1. The graph is mound shaped and there is a mode of 22. The range is from 60 to 65 and there is a outlier on the right side of the graph.
ReplyDelete2. Yes, I commented on the penny on the shelf which could be an outlier in which case it would be considered unusual.
3. The nickel means n=5, it does not belong in the graph because the graph is discussing n=10.
4. The spread and the variability of the have decrease.
5. The Central Limit Theorem the states that if the larger n is in a sample then the more likely the distribution will be normal. When n=25 the distribution it is much more normal.
1. The distribution of the graph is mound shaped, the mode is 22 years, the range is about 60 years, it seems to be skewed to the right and there is an outlier to the right of the graph.
ReplyDelete2. Yes, I commented on the penny. It may or may not be an outlier due to it being somewhat close to the other pennies on the right of the graph.
3. The nickel represents a sample size of mean 5. It does not belong in the graph because the graph is for a sampling distribution of means 10.
4. The spread and variability both decreased. The spread decreased by about 40.
5. The central limit theorem states that as n becomes larger the distribution becomes more normal. When n=25, the distribution is more normal.
1. The distribution is somewhat mound shaped, range is about 65 years, mode is 22 years, the graph is also skewed to the right and there is also an outlier to right of the graph.
ReplyDelete2. Yes, I commented on the penny on the shelf which could be an outlier in which case it would be considered unusual.
3. The nickel was used to represent means of n=5 but the graph is for means of n=10.
4. The spread of the data and variability has decreased. The spread is about 25 now.
5. The Central Limit Theorem states that the frequency plot of the means of random samples will approximate a normal distribution as n increases.
1) The data is slightly skewed to the right and mound shaped there are some outliers.
ReplyDelete2) Yes, that penny on the shelf is an outlier.
3) The nickels represent 5 pennies and the dimes represent 10.
4) As the numbers represented become larger, the more normal the distribution looks.
5) This relates to the central limit theorem because when the pennies were replaced by pieces that represented larger values, the distribution looked more and more normal.