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From the data given below state which group is more variable, A or B?$$\begin{array}{|l|c|c|c|c|c|c|c|}\hline \text { Marks } & 10-20 & 20-30 & 30-40 & 40-50 & 50-60 & 60-70 & 70-80 \\\hline \text { Group A } & 9 & 17 & 32 & 33 & 40 & 10 & 9 \\\hline \text { Group B } & 10 & 20 & 30 & 25 & 43 & 15 & 7 \\\hline\end{array}$$

Intro Stats / AP Statistics

Chapter 15

Statistics

Section 3

Range

Descriptive Statistics

Missouri State University

University of North Carolina at Chapel Hill

Oregon State University

Boston College

Lectures

0:00

02:24

Which of the following cor…

03:52

The following data are for…

01:40

For quantitative data, we …

00:09

Identify the variable or v…

09:02

Check each data set for ou…

07:11

Do the following:a. Gr…

08:27

00:35

Use the test scores below.…

00:13

00:49

a. Is the graph below a ba…

02:35

Which of the following sce…

00:44

00:38

In an experiment, the ____…

01:24

A frequency table for a se…

02:21

Assume that the variable u…

01:48

Refer to the given values,…

01:02

Here are the amounts of mo…

02:04

A class survey Here is a s…

10:52

The data shown represent t…

03:24

The scatter plots show the…

the syringe, Welcome back. And this question I'm given the marks of students group A and group B. And we have to find out which is more variable. Okay, so for that I'll compare two standard deviations of both of them. Okay, so finding the standard divisions, I had just prepared the table for the group A. Okay, and then we'll find out for group B. So I have find out some of the values like via a video of a square for 18 to buy over 8.5 of a into a square. Okay, so you can just create the stable and then I'll found find out all the values now, not that edge, that is the Limits that it's 10. Okay, class limited stent. And is the total number of 3, 20, which is 1:50 and a is 45. Okay, so now, no, no died men of this stable Mean of the stable would be equal to a plus a. In the lower limit of middle part. Right? It is the middle part that as you know, 40 and stays the middle wealth 14th of this, the middle of the these class intervals and uh the middle time of 14th of this. What if I okay, so what they have in the middle, so mean, would be 45 plus submissions I ranging from one to seven x. of I divided by And times of edge, this is a formula of pain, you know that so for things that values, it comes out to the 45, less minus six And to 10. However, did -6 because it is the sum of f of a body of a. Okay, so just putting the value, It comes out of -6 times. Edge divided by end and develop Venice 150. Right? So it comes out to be What We Fight -0.4. Okay, so this mean mean comes out to be 44.6. Now the variance variance would be variants would be equal to at square divided by n square Times of n submission I ranging from 1 to 7 F I via I squared and uh minus submission. Let me draw it correct Submission I ranging from 1 to seven F. F. I while I whole square. Right, this is the formula of variance. So we'll just find out by putting these values. So at square is 100 square is 2 to 5 double zero And N is 150. This submission is three What to do? And this submission is 6-6 square is 36. Right? This is minus six. So minus six square is statistics. So if I just calculated, it comes out to be one upon 2 to 5 times of 51264. Okay, so the variance comes out to be variants comes out to be 227 .84. Okay, so if I can clear the standard division, it would be under root of 2-7.84. So if you just calculated it would be approximately 15.09. Okay, now doing the same thing for uh for group B, I'll just draw this table for group B as well. So this would look something like this. So now you can see this is the table for you know the B part. Right? So this is a table for be back. So let me change these abbreviations. So similarly this in the same way I'll find out the variance of the standard additional big group. Right? So first of all, finding out the mean mean would come out to be a plant summation. I didn't do from 1-7, some mention of effort I via I divided by n kinds of edge. Okay, so it will be seen, that is 45 And if I this is coming out to the same submission, that is -6 and H is 10 divided by and is also saying that is 1.50. Okay, so the mean is coming out to the same, that is 44.6. Right, so now finding out the variance experience would come out to be the same formula variants. So I'll put just the people the values. So it would come out to be 150 times three classics only. This value has been changed. The uh the summation of fo vice square only. This value has been changed to otherwise everything is same. Right? So just calculating it, what do I get is 1.25, I'm just 5, 4 864. Okay, so uh, calculating it, it would come out to be 243.84. That means standard division would come out to be under oath of to 43.84. That is 15.61. So now I have the standard divisions of both developed body groups center division of B. S 15.61 and center division of Abel's 15.9. Right? So you can see that mean of buddha group is same. And the group with the step with the greatest standard division will be more variable, Right? So since B is having more standard deviation than A, so we will be more variable. So that's it. Thank you.

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