Transcript:
Hi, guys, this is. Jonathan Lambert, with the mathematics development and support service at the National College of Arnold and this short video, is going to detail how to construct a histogram from a grouped frequency distribution and well for this particular video. We’re gonna assume that we have a group frequency distribution. In one of my previous videos, we have constructed this group frequency distribution from raw data. So if you are still a little bit unsure about how to construct a group frequency distribution. I would recommend maybe having a look at that particular video, okay, But to construct a histogram from Google Frequency, distribution is pretty straightforward. Okay, and we’ll, let me just grab some graph paper. Okay, so to construct it, we all will always try to construct it on graph paper. Hey, a histogram is basically a chart. There’s a vertical axis and there’s a horizontal axis. Okay, the horizontal axis represents the variable mm-hmm that we were measuring in air case. Facebook friends. Okay, so let’s say Facebook friends or how many Facebook friends an individual has so Facebook friends and this particular axis is graduate it and it’s graduated based on the intervals. Okay, so we can see that Air Force interval begins with a five, so lets. Just actually start here, lets. Just start here. Let’s say this is five. Let’s say it goes to 18 18 then goes to 21 21 goes to 44 44 goes to 57 57 goes to 70 and 70 goes to 83 Okay, So this particular axis here now represents the variable. Facebook friends or how many Facebook friends an individual respondent has and just be careful here. The scale is not consistent as in this represents the distance of five for each one of these intervals represents the distance class width, which is taught in. So I’ll just put that little symbol in here to indicate it’s like a little spring to say that that particular interval here isn’t represents isn’t a representative size and with respect to the others, okay, and the vertical axis represents our frequencies doesn’t have to represent the raw frequencies. It could represent relative frequencies or percentage frequencies for Ferrer purposes. It’s gonna represent our frequencies. So we symbolize that by small F, which is the number of people or the number of respondents. Yeah, okay, number of respondents. Yeah, which is our frequency and we’ve seen as a maximum number of respondents in any particular interval is 14 so what we could do is we could go up in in the intervals to to get to 14 If we said that this was let’s say 3 6 9 12 15 That would do, let’s see. Can we do any better make it try to use as much of the object? This space as possible, 2 4 6 8 10 12 14 If we want to us 2 4 6 8 10 12 14 That’s a little bit more representative. So it’s 2 4 6 8 10 12 14 Okay, so we’ve represented both of our axes. Okay, now what we do is for each one of our intervals. We create a bar of the appropriate height now. In our particular instance, here, each of our classes has the same class width, so with a 14 they don’t necessarily have to have the same class with. But what is important is that our unit of measure. Let’s say our class width times. Our how many times the A the class width is within the interval times. Our frequency represents the area of the bar. Okay, but that’s not complicated and lets. Just consider this particular scenario. Every class has the same width, so each class is gonna have a height specified by its frequency. So between 5 and 18 we’ll have a bar of height 4 so between 5 and ATM. I have a bar of height for between 18 and 41 will have a bar fights 10 between 21 and 44 We have a buyer of heights 12 between 44:57 We have a barrel of hype. 14 Between 57 and 70 We have a barrel of height 9 That’s in around here. And between 70 and 80 3 We have a barrel of heights. Tre, which is in around here somewhere. OK, and we joined ears up like so to create what is called a histogram, right. Histogram is just another representation of our distribution. Okay, in this particular situation here. Our distribution is represented in a table which we call a group frequency distribution. These 52 values could be represented as raw data. May that’s still the distribution, but it’s raw data and in this situation here that’s represented in a chart and this chart is a histogram and it’s straightforward to calculate or to create a histogram. Okay, it’s a straightforward case history. Once we have the group frequency distribution. Some things to know about the histogram is its shape. The shape of this histogram seems to be relatively normal. Hey, that’s important for us. And so from this particular perspective, you could you could. I suppose esta me. And the average or the meaning of this particular distribution from the histogram, but because we have a normal curve plotted over and well, the one the properties of normal curve is that the mean is down the center. So maybe the mean down the center will be down here, So maybe the mean of this particular distribution is in. We could estimate it being around 44 Okay, so that was a how to create a histogram from a group frequency distribution. I hope that was helpful. This was Jonathan Lambert with the mathematics development and support service at the National College Environment.