The following are the machined diameters (mm) of 58 metallic...

The following are the machined diameters (mm) of 58 metallic bars produced in a manufacturing unit: 726 945 863 673 876 842 645 942 621 833 1042 526 735 893 621 773 531 733 635 998 954 763 1073 550 725 1084 747 849 716 1032 721 962 683 768 872 632 787 641 752 800 1063 794 1062 613 714 867 590 749 854 943 1021 681 943 842 841 730 961 982 Group the data into suitable set of intervals and draw the following: \begin{itemize} \item a histogram and \item a cumulative frequency curve indicating the upper and lower quartile boundaries. \end{itemize} Also find: \begin{itemize} \item Mean, \item Median \item Mode \item Variance & \item Standard Deviation \end{itemize} Comment on whether the symmetry of the distribution is likely to be a normal distribution and what measure might best describe the central tendency in this case.

Transcript

00:01 Here we have some data, and this data represents the diameters of n equals 36 rivet heads in one hundredths of an inch.

00:14 So these are all in units of one hundredths of an inch.

00:18 So what that means is this, 6 .72 is 6 .72 one hundredths of an inch.

00:27 That's how we interpret that.

00:28 And so what we want to do today is make a qq plot.

00:35 So that means we're going to have a little plot here.

00:40 And we're going to use technology to do this.

00:44 It's incredibly cumbersome to do strictly by hand.

00:47 So we're going to have essentially z -scores being this axis here, and this is going to be theoretical z -scores.

00:56 And then we're going to compare those to our actual data z -scores so we'll have our data z -scores and then we'll get some points and ideally we want them to follow along a straight line that means in terms of ideally in the sense that the data would be normal then we can assume that as normal so let's go and do that and we're gonna use excel to do this work so here we go so here's the the data as it's presented to us what we need to do is sort it and i'll talk us through this stuff here in a second so you take your data and you sort it that's what we've done here like that and then we're going to rank it and the rank this is part this is the going to tell us what the theoretical z -scores are going to be so here's the rank and the way you do this you don't you can't just rank it 1 to 36 because some of these have are the same value right 6 .62 6 .66 there's a few of those and you count so the rank is how many of the you know in this case these two are both one right 6 .62 is one 6 .62 is also one so they're still the first rank they happen to be the same one but that's okay this is the third we skip two because these two data points, they share the same rank, but there's no second place because this is the third, because this is the third data point, so it's rank 3.

02:41 Whereas these four 6 .66s are all ranked 4 because there's four of them, and that falls next in the value.

02:53 Well, likewise, for 6 .67 is rank 8, because this number, 6 .67, is the eighth number, and that's why it's here.

03:02 There's no other 6 .67s.

03:04 Anyway, and this is the formula to do that.

03:06 Rank j9 is the cell.

03:09 This stuff here is the data range, like that.

03:13 And then 1, this tells us we want to go descending.

03:16 You could do 0 and have it, or 0 is descending, which means it's going to go, you could have it be 0 and copy and paste that down but we want to go 1 means ascending so the rank now we want to get the percentile so the percentile is you take the rank that number minus .5 divided by the count divided by 36 and that's going to give us the percentile so that's what we do down here and we just you just copy and paste it all the way down and then this is the theoretical z score here now the z scores are calculated um sorry these are theoretical um so these are found by using this norm s i and v and then you put in the cell reference and this is um giving you the z score that corresponds with that probability so in a z distribution distribution, if you've got some value here, we'll call it v0, this area, let's say this is 0 .01, that corresponds with some z score, z0, and this is the theoretical z value.

04:54 And this area here, this 0 .01, this is the percentile value.

05:01 That's what this is, the percentile.

05:13 And so this number is.

05:14 And that percentile is going to give us the z -score.

05:16 And that norm s, i, and v function spits out that theoretical z -score.

05:22 And you do that all the way down.

05:23 Just copy and paste that formula all the way down...

Question

Please give Ace some feedback