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How the scores are distributed/scattered around the central tendency is defined by:KurtosisVariabilityCentral tendency onlySkewness...

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How the scores are distributed/scattered around the central tendency is defined by:KurtosisVariabilityCentral tendency onlySkewness

How the scores are distributed/scattered around the central tendency is defined by: Kurtosis Variability Central tendency only Skewness



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Which statistical measure of central tendency is most affected by extreme scores? a. Mean b. Median c. Mode d. Skew e. Correlation

And this problem, it is a instagram of a set of data indicates that the distribution is skewed right now. We need to determine which measure of central tendency will be larger, the mean or the media, and we need to explain why. Now I know that whenever the mean is a lot larger than the median in this case the shape of the distribution is that the distribution is skilled, right. On the other hand, if the mean is a lot less than the median, then the distribution will be skewed left, and if the mean is roughly equal to the medium, in that case the distribution will be symmetric. Now in this case it is said that the distribution is cured right? This will mean that the mean is greater than the median. So the answer to the question which measure of central tendency will be large at the mean or the media? Yeah, I'm telling me the me and the reason is that any distribution and with the mean is a lot larger than the media will be skewed right? And the distribution of the data in this case is huge. Right against me will be larger.

Now here on this problem, we have been told that we have a history gram of a set of data and the distribution of the data is skewed right? It is skewed right now, what it means to be skewed, right, is that the mean is substantially larger laying the medium? Okay. The mean is substantially larger than the median. Is there something that you'd write would look something like this? So you'd have your median here? Yeah. And then you're me you don't have to be somewhere over here. And so the question at hand asked us which measure of central tendency will likely be larger than mean or the median? And so just by that definition of being skewed, right, that means we would expect them mean to be substantially larger.

Okay, So this is not question with this problem. Doesn't ask us any calculation or computation. It's really just, uh, understanding of mean median and is a mode or midrange mid range. So me, me median mode and minerals and how they represent the measure of center of the population. So what is the center? Well, center can mean many things. It has many formal definition and, uh, mathematics or statistics. So we're gonna break it And formal definition. So not something you should. Okay, I think is a very hard core definition, but something to give you an idea. So it wants to a measure of sanitary wants toe measure, the general tendency, the general tendency tendency off a sample or population. So basically, those measure of center, they want toe tell you we're more around. What value do most of the population like What? What's that? What's the general tendency of the population? So let's start with the me eso so the mean will take every the formal definition is you add up every value that you have, and you divide by the number of values that you have. So how does the mean measure the general tendency of a sample. Well, you basically take every value that you have by dividing it. You get three average score, so the means which is informally the average. And if you have a good enough sample, the mean will will basically, uh, basically tell you on average, like the average average individual in that population. All right, What what's his value for? For this feature for this statistic? So let's take, for example, so theatric judge could be considered as Let's let me write it down the average, uh, individual, the average value at four, the future of which we had to mean the average value for the future. Uh, so for a a random, hopefully, hopefully a random individual, uh, in that population has value close to than me. So it can give you an idea. For example, if you like movies and your great movies on a scale of 1 to 10. And the average rating is seven, for example, that the mean off all movie rating is seven. That means that if you go uh huh to the movie theater to watch something. Hopefully, the movie you will see is close to a seven. It it might be around the seven. Of course, it depends on many things, but that's what the average want to say. The mean is the median is you want 50 percent of your data is greater or equal to medium, and 50% of your data is small or equal, lesser or equal to the media. So it's not exactly like the mean like let's take an example of movie ratings. Uh, if if the main media movie rating is six, that means that half of the movies are, uh, at six, or let half of the movies are six or less, and half of the movies are six or higher. A six out of 10 are higher, so it doesn't really indicate, uh where that then a random an individual might land it just. It just said that if you take a movie, it will either beat. There's a 50% chance that is above a six or 50%. If you pick a random movie, there's you have 50% chance. That is above six out of 10 and 50% that it's below six out of 10. So it's really a way toe and gauge. Uh, if if you you. Basically, you hate most movie the median score for for your movie might be, Let's say, three. If you hate everything you watch, then that means there is a 50% chance that so that most movie that you like would be between zero and three. But it doesn't give indication. Where are they all zeros or all they are are all they mostly threes, whereas with the mean you cannot say, like, well, 50% off the movies? I like our bolos six or above seven. It doesn't that mean doesn't work like that. The median can help you gauge a probability. Demoed is what appears the most often, uh, so let's take another example. Uh, let's take, for example, example, the number of goals scored by hockey players. Eso If you If you look at every hockey player in the NHL, for example, you would see that, uh, for a on the season, some player might score on Lee. One goal to would have that in 100 players score. One goal at it made me two goals would be scored by 60 players, players that don't play very often, and then you would have very large number, you would maybe have only one player who would score 60 goals in this season's Onley One. Uh, but the amount of goals scored the most often would probably, I don't know, maybe around 10 11 12. I don't really know those statistics, but it's what appears the most often. So let's say that and you have 1000 player in the NHL, it's not the right number. It's more than that or less. I don't know. Let's say you have 1000 player who played one game in the NHL for at least one game in the NHL, and you have out of them 700 scored three goals. That means that the modus three goals so it doesn't it doesn't give any tendency like it doesn't ah, give any probability if the mode let's say, have only you take a sample of let's go back again to the movies. You take 10 10 movies and you rate five of them zeros, four of them AIDS, and 19 the mode will be zero. So that means that zero is your most common rating. But it doesn't mean it means that. Okay, Generally, you don't like the movie But it doesn't. It doesn't mean that like, Well, it doesn't say that when you re like a movie, you really like a movie. So it lacks a bit of nuance for smaller data set. And finally, the mid range. The mid range is very rarely used. Uh huh. It it's the minimum value and the maximum value in your data set invited by twos and is in value in the middle. And that that measure is a big like it. It's not incredibly useful. Ah, it's final example with movie ratings. So you write movies on a scale of 1 to 10. Well, that didn't the are honest of 0 to 10. So the minimum rating is zero, and the maximum reading is 10 so the mid range is five. So it's the value in the middle. That value in itself doesn't mean anything, because you don't. You only use two ratings out of maybe 1,000,000 movie ratings that you, uh, that you made so that the mid range should be used very sparingly and shouldn't You shouldn't try to give too many interpretation to the mid range because it doesn't really take advantage of the data you have. It's just look at extreme values and says What's in the middle? So in short, the center, a measure of centers and measure that tries to exhibit a general tendency of a sample or a population the mean well, and that means the average and and non statistics vocabulary. And hopefully, if you pick any random individual that that the goal of the mean in a good sample or well distributed population is that the an individual random individual in that population there will have will be close to the meat. So not exactly the me, but not too far. The median, uh, tells you, uh, help you create a probability. So you you know that in a data set, if 50% of your data will be a greater or equal to the median, and 50% will be lower or equal to the media. So if that the median is very high, that means most of your value of very high. And if the media is very low, that means most of their values are very low. By most, I mean at least 50%. The mode tells you the most re occurring values that the value that appears the most often. So we should be there. But then again, it doesn't give any, uh, education of the distribution or where the other value lies or the frequency of other values. Eso If you have a zero, which appeared for four times, one appears three times to appears three times, then zero is the mode. But it won into are very close, and that is not reflected in the mode. And the mid range is simply the central value off. Your data said. If you only consider the two extreme values so that the mid range is extremely sensitive, toe to changes of highest and lowest value in your data set and it doesn't consider anything in the middle, which makes it more, I guess, a tool toe to use, combined with other central measures.

This question asked from the mean median mode. We know the mean is equal to the number. The sum of all the total numbers, divided by how many numbers that are so add up. Each of the numbers divide by five because there's five numbers and we got 105 Next, we know we're looking from a median, which is the number of the middle. The number in the middle is 98. There's two numbers below in two numbers above 98. Now we're looking for the mode, which is the number that occurs the most often we know 98 occurs the most often, therefore it's the mode. And then we know the the best measure of central tendency would be the median and the reason why? Because we have an outlier, which is 134.


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