Standard Deviation - Explained and Visualized Jeremy Blitz-Jones 2015-04-05 | The video above is more focused on the concept. This other one explains how it's calculated: youtube.com/watch?v=WVx3MYd-Q9wVideo transcript:"Have we discovered a new particle in physics?Is a manufacturing process out of control?What percentage of men are taller than Lebron James? How about taller than Yao Ming?All of these questions can be answered using the concept of standard deviation. For any set of data, the mean and standard deviation can be calculated. For example, five people may have the following amounts of money in their wallets: 21, 50, 62, 85, and 90. The mean is $61.60 and the standard deviation is $28.01. How much does the data vary from the average? Standard deviation is a measure of spread, that is, how spread out a set of data is. A low standard deviation tells us that the data is closely clustered around the mean (or average), while a high standard deviation indicates that the data is dispersed over a wider range of values. It is used when the distribution of data is approximately normal, resembling a bell curve. Standard deviation is commonly used to understand whether a specific data point is “standard” and expected or unusual and unexpected. Standard deviation is represented by the lowercase greek letter sigma. A data point’s distance from the mean can be measured by the number of standard deviations that it is above or below the mean. A data point that is beyond a certain number of standard deviations from the mean represents an outcome that is significantly above or below the average. This can be used to determine whether a result is statistically significant or part of expected variation, such as whether a bottle with an extra ounce of soda is to be expected or warrants further investigation into the production line. The 68-95-99.7 rule tells us that about 68% of the data fall within one standard deviation of the mean. About 95% of data fall within two standard deviations of the mean. And about 99.7% of data fall within 3 standard deviations of the mean. The average height of an American adult male is 5’10, with a standard deviation of 3 inches. Using the 68-95-99.7 rule, this means that 68% of American men are 5’10 plus or minus 3 inches, 95% of American men are 5’10 plus or minus 6 inches, and 99.7% of American men are 5’10 plus or minus 9 inches. So, this means only about .3% of American men deviate more than 9 inches from the average, with .15% taller than 6’7 and .15% shorter than 5’1. This reasoning suggests that Lebron James is 1 in 2500 and Yao Ming is 1 in 450 million. In particle physics, scientists have what are called 5-sigma results, results that are five standard deviations above or below the mean. A result that varies this much can signify a discovery as it has only a 1 in 3.5 million chance that it is due to random fluctuation. In summary, standard deviation is a measure of spread. Along with the mean, the standard deviation allows us to determine whether a value is statistically significant or part of expected variation."
How to draw a histogram from a set of data Jeremy Blitz-Jones 2020-11-18 | Step-by-step guide for how to create a histogram from a set of data.Video transcript:I recently looked up local dogs that are up for adoption. I found that the dogs had a range of weights. Many dogs were the kind you could fit in your bag and some were too big to sit in your lap.To better understand and visualize this data on local dog weights, we can create a histogram. Start by drawing the y-axis which is always the number of data points, in this case the number of dogs. Then draw the x-axis which represents our variable: dog weight. When drawing the x-axis, we need to decide what intervals or bin sizes we should use for the dog weights. For example, we could use increments of 5 pounds...or increments of 10 pounds. Let’s start with bins of 10. So our labels would be 0-10 pounds, 10-20 pounds, and so on. Some histograms label the ranges while others label only the boundaries.Next, let’s sort our dog weights from smallest to largest. Then, in each bin, we put how many dogs are within that range. The first bin is 0-10 pounds. There is a 5-pound dog, 6-pound dog, 7-pound dog, and three 8-pound dogs for a total of six dogs in the 0-10 pound range. So the first bar for 0-10 pounds has a height of six. Next, count how many dogs are in the 10-20 pound bin. There are 8 dogs in this range. So the 10-20 pound bar has a height of 8. There are only two dogs in the 20-30 pound range so that bar has a height of two. There’s a dog weighing 31 pounds and a dog weighing 40 pounds. Does the 40 pound dog go in the 30-40 pound bin or in the 40-50 pound bin? The convention is to put borderline values in the upper bin, so the 40 pound dog would be put in the 40-50 pound range rather than the 30-40 pound range. So each bin includes the bottom value in the range but not the top value, in this case 30 to 39 pounds. This means for our 30 to 39 pound bin, we only include the one 31 pound doggo. Our 40 to 49 pound bin gets the 40 and 45 pound dogs. In our data set, there aren’t any dogs in the 50-59 pound range so we’ll skip it and add our last dog to the 60-69 pound bin and draw a bar with a height of one. Congratulations! You now know how to draw a histogram for a set of data. Now let’s explore how different bin sizes affect the look of the histogram and the story the data tell. First, let’s reduce the bin size to intervals of 5 pounds. We can now see more details about the data, which is useful for the dogs between 5 and 20 pounds but looks a bit silly for the remaining weights where it just shows us that there is one dog in some of the other weight ranges. Let’s try a larger bin size of 20 pounds. This conveys the main trend which is that there are many more lighter weight dogs, but it doesn’t allow us to differentiate between 0-10 pound dogs and 10-20 pound dogs like we could before. As you’re noticing, with histograms, there’s no way to know where within each bin a data point falls, so we don’t know whether the one dog in the 60-80 pound range is 60 or 79 lbs. It seems the 10 pound bins are probably the best choice for this data set because they give a sense of the trend and also enough detail for someone considering adopting a dog.Have fun visualizing your data!
Addition Rule of Probability - Explained Jeremy Blitz-Jones 2020-10-05 | The addition rule of probability can be used when you need to calculate the probability of A “or” B occurring:P(A or B) = P(A) + P(B) - P(A and B)VIDEO TRANSCRIPTWhat’s the chance of drawing a heart or a face card? If some students play soccer, some play tennis, and some play both, what's the probability that a student selected plays at least one of the sports?To answer these questions, we can use the addition rule of probability. It can be used when we’re interested in at least one of multiple criteria to be true, and also when we’re interested in the probability of A “or” B. Rolling a two OR a five. Drawing an 8 or a spade. Having an android phone Or an iphone.We’ll start with two mutually exclusive events, which means they cannot both occur. For example, rolling a two OR a five. It’s not possible to roll a two and a five in a single roll. The addition rule of probability says that the probability of at least one of two mutually exclusive events occurring is simply the probability of the first event plus the probability of the second event. This is why it’s called the addition rule of probability. For rolling a two or a five, we would calculate the probability of rolling a two (1 out of 6) and the probability of rolling a five (1 out of 6) and add them together...2 out of 6. This works well as long as the events are mutually exclusive. Let’s look at a second example. What’s the probability of drawing a heart or a face card? This is slightly more complicated because the events are not mutually exclusive—it’s possible to draw a queen of hearts which is both a heart and a face card. So we add one more element to our original formula. After adding the probability of event A and the probability of event B, we then must subtract the probability of event A and B to avoid double counting. If we count 13 hearts, and then 12 face cards, we’ve counted the jack, queen, and king of hearts twice. So we must subtract the number of cards that are both hearts and face cards in our formula.You could also visualize it as a venn diagram of hearts and face cards. To calculate the total area, the easiest way is to add both circles together and then subtract the overlap. As a final example, consider a group of students. 50% play soccer, 20% play tennis, and 10% play both soccer and tennis. What’s the probability that a student selected plays at least one of the sports? We can reword the question as what’s the probability that a student plays soccer OR tennis? This includes the students who play both. To answer this, we can use the formula. We add the probability of playing soccer to the probability of playing tennis and subtract the probability of playing both. The result is a 60% chance that a student selected at random plays at least one of the two sports.In summary, if you want to know the likelihood of event A OR event B happening, or the probability that at least one of multiple events will occur, you can use the addition rule of probability.Correction:3:46 The formula should be P(A or B) = P(A) + P(B) - P(A and B).
The Multiplication Rule of Probability - Explained Jeremy Blitz-Jones 2019-04-08 | Any time you want to know the chance of two events happening together, you can use the multiplication rule of probability. Independent events:P(A and B) = P(A) x P(B)Dependent events:P(A and B) = P(A) x P(B | A)...where P(B | A) is the probability of event B given that event A happened.Have other topics you'd like to see a video on? Let me know in the comments!Video transcript:What’s the chance of rolling snake eyes? What’s the chance of flipping heads three times in a row?When calculating the probability of two or more events happening together, we can use the multiplication rule of probability.We’ll start with independent events where one event’s outcome has no effect on the other event’s outcome. For example, what’s the probability of rolling snake eyes? Each roll is an independent event because the value on one die has no influence on the value of the second die. The multiplication rule of probability says that the probability of two events A and B happening together is the probability of event A multiplied by the probability of event B - in this case, the probability of rolling a 1 on the first die, multiplied by the probability of rolling a 1 on the second die. This is the case if you’re rolling the dice together or one at a time. The probability of rolling a 1 on a die is one out of six, so the probability of rolling a 1 on both dice is ⅙ times ⅙. Across all 36 possible rolls of two dice, one of them is snake eyes.Let’s look at a second example - what’s the probability of flipping heads three times in a row? Well, it’s the probability of the first flip landing heads, multiplied by the probability of the second flip landing heads, multiplied by the probability of the third flip landing heads. ½ x ½ x ½ = ⅛. What if the events are dependent? What if the second event’s probability is based on the outcome of the first event? In this case, the probability of the events happening together is a little more complicated - the probability of event A happening multiplied by the probability of event B happening given that event A happened. For example, what’s the probability that you’ll draw an ace, hold onto it, and then draw a king? In this case, we’ll start with the probability of drawing an ace: four out of 52 cards are aces. Then, we need to calculate the probability of drawing a king, given that we’ve already drawn an ace, which is different than the probability of drawing a king from a full deck. There are four kings left in the deck, and there are 51 cards remaining since we’re holding onto an ace. We multiply these two probabilities together and we get a probability of 16/2652, about a 1 in 167 chance.In summary, if you want to know the likelihood of event A and event B happening, you can use the multiplication rule of probability. Make sure to identify whether the events are independent or dependent and adjust your calculation accordingly.
Math Puzzle: The Miller and the Butcher Jeremy Blitz-Jones 2017-08-09 | A miller uses a 40 lb rock to measure grain with a two-sided scale. He lends the rock to his friend the butcher. The butcher comes to return the rock and says, “I’m sorry but I dropped the rock and it broke into 4 pieces.” Upon seeing the pieces, the miller says, “Actually, this is great. With these 4 pieces I can measure any amount of grain from 1 to 40 lbs!” What are the weights of the 4 pieces?
How to Calculate Permutations and Combinations - Probability Jeremy Blitz-Jones 2016-11-10 | Animated explanation of how to calculate permutations with repetition, permutations without repetition, and combinations without repetition. Useful when trying to calculate probabilities.How much more secure is a 6-digit passcode than a 4-digit passcode?How many different two-card hands could you get in Texas Hold ‘em?How many different outcomes are there for the 100m final?All of these questions can be answered using permutations and combinations, which are part of the field of mathematics awesomely called combinatorics and less awesome called counting.When working with permutations and combinations, we need to ask two questions to begin solving the problem: “Does order matter?” and “Is repetition possible?”
Beginner Blender Tutorial - Introduction to Camera Tracking - aka How to Showcase Your 3D Model Jeremy Blitz-Jones 2016-09-23 | This tutorial demonstrates how to show off a completed 3D model using camera tracking.
How to Calculate Standard Deviation Jeremy Blitz-Jones 2016-09-23 | Follow these five steps to calculate standard deviation. Also includes the standard deviation formula.Here's the video transcript:"How to Calculate Standard DeviationHow many vegetables do you have in your fridge? Is that a common amount or are you an outlier? We can use standard deviation to know whether someone’s behavior is normal or extraordinary. Standard deviation, often calculated along with the mean of a data set, tells us how spread out the data is. It is used for data that is normally distributed and can be easily calculated using a graphing calculator or spreadsheet software, but it can also be calculated with a few math operations.We’re going to use an example involving the number of vegetables five of our friends have in their fridges. They have 2, 3, 4, 7, and 9 vegetables.To calculate the standard deviation, the first step is to calculate the mean of the data set, denoted by x with a line over it, also called x-bar.In this case, the mean would be (2 + 3 + 4 + 7 + 9) / 5 = 5. Our average friend has 5 vegetables in their fridge.The second step is to subtract the mean from each data point to find the differences. It’s helpful to use a table like this. 2 - 5 = -3, 3 - 5 = -2, 4 - 5 = -1, 7 - 5 = 2, and 9 - 5 = 4. The third step is to square each difference. (This makes all the differences positive so they don’t cancel each other out and it also magnifies larger differences and minimizes smaller differences.)-32 = 9, -22 = 4, -12 = 1, 22 = 4, and 42 = 16. The fourth step is to calculate the mean of the squared differences.(9 + 4 + 1 + 4 + 16) / 5 = 6.8.The final step is to take the square root. (This counteracts the squaring we did earlier and allows the standard deviation to be expressed in the original units.)The square root of 6.8 is about 2.6 and that’s the standard deviation.We're done! The mean number of vegetables is 5 with a standard deviation of 2.6 veggies. Knowing that about ⅔ of the data fall within one standard deviation of the mean (assuming the data is normally distributed), we can say that about ⅔ of our friends have between 2.4 and 7.6 vegetables in their fridges.To recap, these are the five steps for calculating standard deviation:1. Calculate the mean. 2. Subtract the mean from each data point.3. Square each difference.4. Calculate the mean of the squared differences. 5. Take the square root.Using symbols, the equation for calculating standard deviation looks like this [see video]... Lower case sigma stands for standard deviation of a population.Upper case sigma tells us to calculate the sum for each instance.X is each data point.X bar is the mean of the data points.And n is the number of data points. Keep in mind that there is a similar formula that divides by n-1. That formula is used when you only have data for a sample of the population. Hope this was helpful. See you next time!"
Low Poly Rose Timelapse (Blender v2.76) Jeremy Blitz-Jones 2016-03-05 | Tutorial video: youtube.com/watch?v=V_iNNrvonxoMusic: Don't Stop by Audionautix is licensed under a Creative Commons Attribution license (creativecommons.org/licenses/by/4.0)Artist: http://audionautix.com
Blender Beginniner Tutorial: Low Poly Rose Jeremy Blitz-Jones 2016-03-05 | This is a tutorial showing how to model a low poly rose.
Beginner Blender Tutorial: Wood Table (Boolean Modifier and Wood Texture) Jeremy Blitz-Jones 2016-03-03 | This tutorial shows how to use the boolean modifier and add a wood grain texture.
Blender Beginner Tutorial - St. Louis Gateway Arch (Blender 2.76b) Jeremy Blitz-Jones 2016-02-29 | This Blender 3D modeling tutorial goes over how to create the St. Louis Gateway Arch.
Law of Large Numbers - Explained and Visualized Jeremy Blitz-Jones 2015-11-26 | Video transcript:How does an insurance company decide how much to charge for car insurance?How do casinos set up payout structures to make sure that they make a profit?How does a poker player decide whether or not to fold?How do we efficiently measure the appeal of a political candidate?The answers to these questions are informed by the law of large numbers.The law of large numbers states that as the number of trials or observations increases, the actual or observed probability approaches the theoretical or expected probability.This is important to understand because it allows us to predict and have confidence in how events will play out in the long run.Let’s take a common example—flipping a coin. Assuming the coin is fair, we know that the theoretical probability of flipping heads is .5 or 50%. However, that doesn’t guarantee that if we flip a coin 10 times we’ll get 5 heads. But we can be confident that as we continue flipping a coin indefinitely the cumulative proportion of heads flipped should get closer and closer to 50%. Looking at this graphically helps to illustrate the concept. I just flipped a coin 20 times and these are the results. After each flip, we’ll calculate the cumulative proportion of heads so far. So the first flip is tails, so our current proportion is 0 heads out of 1 flip—0%. The second flip is also tails, so now it’s 0 heads out of 2 flips— still 0% heads. Next flip is tails again— 0%. Then heads, now we have 1 heads out of 4 flips— 25% heads. Flip again and it’s heads—40%. Heads again and we finally hit our theoretical probability of 50% for the first time. Let’s keep going…(video plays out the rest of the 20 flips). This graph shows the observed probability approaching the theoretical probability. One common misconception, referred to as the gambler’s fallacy, is that if the first four flips were tails, you’re more likely to get heads on the next flip because the proportion is supposed to even out to 50% heads. This is not the case because each flip of a coin is an independent event, its outcome is unaffected by all previous events. So if you start out with four tails in a row, it’s not that you are more likely to get heads, it’s just that in the grand scheme of things, four tails flips will get averaged with a huge number of flips that are expected to yield an even number of heads and tails, causing the proportion to approach 50% as the number of trials increases.Another version of the law of large numbers explains that the more people from a population that you sample, so the larger your sample size, assuming your sample is free from bias, the closer your sample average will be to the population average. Let’s say you have a group of 100 people. Each has some number of dollars in their wallet. If we ask one person how much money she has in her wallet, we’ll get our first observation ($49), which might be pretty far from the average of the group. After asking the second person ($29) and averaging that value with the first ($30), we are likely to have a better estimate of the group average. As we continue this process of adding observations and thereby increasing our sample size, we’ll generally get better and better estimates of the group’s average. SUMMARYSo the law of large numbers gives us a compass with which to navigate the randomness around us. Even though we can never predict the outcome of a single coin flip, we can know that over time about half of the flips will be heads. This knowledge underpins insurance, gambling, and investing. And in general, the principle supports the idea that a well-founded strategy that is followed consistently should win out over time, even though it might result in a few negative events along the way.
Airfoil Blender Tutorial for 3D Printing Jeremy Blitz-Jones 2015-10-01 | How to model an airfoil fin to be 3D printed for a model rocket.
Using TI-83 Plus to find linear regression equation and predict values Jeremy Blitz-Jones 2015-09-30 | ...
Monty Hall Problem Explained with Four Solutions Jeremy Blitz-Jones 2014-03-30 | Explanation of the Monty Hall Problem with four solutions.Play the game at http://www.stayorswitch.com
