6 th Grade Math Chapter 12 Lesson 4 Shape of Data Distribution

hello everyone welcome to chapter 12 lesson 4 it says predict two things we'll learn about the shape of the data distributions so some terms are going to be going over today our clusters peaks gaps in symmetry to describe the shape of distribution distribution of data can be described by the spread so we're going to be going over some vocabulary the distribution of set of data shows the arrangement of data the data values the words below show some of the ways the distribution of data can be described match the words below to their definitions so we have cluster gap peat and symmetry so the left side of the distribution looks like the right side that's going to be symmetry when it's zip symmetry that means or symmetric that means both sides are pretty much the same the numbers that have no data values that's going to be where we have gaps where there is no data the most frequently occurring values or mode that's where we're gonna find the peak and the data that are grouped closely together is going to be cluster so when things are clustered together means it's close together so the real world bleep the line plot shows the cost in dollars for parasailing for the different companies on certain Beach draw vertical line through the middle of the data what do you notice if draw vertical line noticed the left and right side are the same some must say left and right side for the same so the these have would be symmetric use one of the root zone to write sentence about the data so another thing that we also notice is there are no gaps there moving on so describing the shape of distribution so data that are evenly distributed between the left and right side are symmetric distribution the distribution shows shown has cluster of several data values within the rent in full interval of ten to twelve the gaps nine and thirteen have no data values the value of ten is at its peak because it's most frequently occurring value so this is pretty good example so the left and right side are not symmetric but we do have cluster here because we have group that's close together we have gaps at nine and thirteen and our peak is same as mode is at ten because it appears most frequently so example when it says described shape of it each distribution the line plot shows the temperature in degrees Fahrenheit in city over several days so know the things we can use we do have two clusters we have gap and then we also have peak so it says you can use clusters gaps peaks and outliers and symmetry to describe the shape okay so will be here symmetry so so we're gonna be using lot of different terms this is the shape of the distribution is not symmetric because the left side of the data it does not look like the right side of the data so that's how they are describing symmetry so what said here earlier just ignore so it's not symmetric there is gap between 19 and 21 which we I've already stated there are clusters from 16 to 18 in 25 to 225 the distribution is peak of 22 and there are no outliers so we want to make sure we hit all of these so we have to state whether it exists or if it doesn't exist so example 2 the box plot shows the number of visitors to gift shop in one month so with box plot we it's important to know that we cannot identify gaps because we know what the box plot we just know the data is in between here so we cannot identify the gaps in box plot we also cannot identify Peaks or clusters each box and whisker has the same length so the data is evenly distributed the distribution is symmetric since the left side looks like the right side and there are no outliers it's the only thing that we have for the box this specific box plot is that it's symmetric so Part says describe the data so used clusters gaps and Peaks outliers symmetry describe the shape of the distribution of the right so go ahead and pause the video and do that now so right off the bat you can say the data is not symmetrical because if they're symmetrical it would be the same on each side so it's not symmetrical and then we have cluster here is this where most the data is understand there is data here but it's not that much so there is cluster from 0 1 to 730 there are no gaps there's Pete at 0 1 2 to 30 so clusters gaps Peaks and they're not letters so the next thing is the key concept measures of center and spread use following flowchart to decide which measures of center and spread are most appropriate to describe data distribution so the first question we have to ask is the data distribution symmetric if yes use the mean to describe the center use the mean absolute deviation to describe the spread if it's no use the median to describe the center use the IQR to describe the spread well know which one requires lot less work this is if there is not liar the distribution is not usually symmetric so this is where we're gonna be going to key concept to find out the the answers for the rest for the measures of center so let's look at example 3 the number the line plot shows the number of states visited by students in the class choose appropriate measures at center to describe the center I'm sorry choose the appropriate measures to describe the center and spread of the distribution justify your response based on the shape of distribution so we know it's not symmetric so if it is not symmetric we're gonna be using the median to describe the center and I'm going to use IQR to describe the spread so the data is are not symmetric and there is an outlier 19 the median and IQR are appropriate measures to use so write few sentences describing this center and spread of the distribution using the appropriate measures so we're going to find the median so we have 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 so we're at 19 then we're gonna want to use ten the tenth number because they'll be nine on the left and 9 on the right it's one two three four five six seven eight nine ten so our median is gonna be twelve states the first quartile is 11 and third quartile is 13 so the to the interquartile range 13 minus 11 or two states the data centered the data are centered around 12 States the spread of the data of the center is about two states so go ahead and try choose the appropriate measures to describe the center and spread of your distribution just fire response based on the shape of the distribution then describe the center and spread so go ahead and pause the video okay so after looking at it this is symmetrical it is the same on the left and the right so we're gonna be you need to find the mean but after all of your hard work you should get 29 years in the mean absolute deviation you will be getting 1 and 7/10 years and I'm gonna say asymmetrical cannot smell symmetrical that's why yeah and that's the lesson so thank you for watching