Problem

The following data were used to construct the his…

01:44

Problem 19 Easy Difficulty

The Los Angeles Times regularly reports the air quality index for various areas of South-
ern California. A sample of air quality index values for Pomona provided the following
data: $28,42,58,48,45,55,60,49,$ and $50 .$
a. Compute the range and interquartile range.
b. Compute the sample variance and sample standard deviation.
c. A sample of air quality index readings for Anaheim provided a sample mean of $48.5,$
a sample variance of $136,$ and a sample standard deviation of $11.66 .$ What compari-
sons can you make between the air quality in Pomona and that in Anaheim on the basis
of these descriptive statistics?

Answer

a) $32,10,$
b) $s^{2}=2.75, s=9.63068,$
c) Same air quality average, higher spread of index in Anaheim.

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Descriptive Statistics: Numerical Measures

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Video Transcript

are right for apart A. We're going to make an UN group frequency distribution. So I'm gonna start five, listing the possible AP scores in the X column. So one to three for and five. And then next to that, we need to find the frequency of each of those values in the data set and write that in the frequency column. So there were nine scores of one. There were 11 scores of to. There were 13 scores of three. There were six scores of four and there were three scores of five. Now we're going to make our frequency, hissed a gram. So we have to make sure that we title the X axis with AP scores. And then we list the AP scores 1234 and five. And then the y axis is our frequency. And for the scale I counted by choose here. Our graph also needs a title. So we'll do 42 AP scores in 2007 to 2008. Ah, Pearson Unified. Okay, so now we need to make our bars. So, for our bar of an AP score of one needs to have a height of nine or frequency of nine, and we've made our first bar there for one. Now we're going to do our bar of a score of two. And that's whenever frequency of 11. It's gonna be a little bit higher than our first bar. Now with the history Graham, our bars are connected, so that is very important. All right. And then, for a score of three, we have 13. This is gonna be our highest bar. Move our title there for a bar of four. We're gonna have a frequency of six. And lastly, our score of five has three. And the important thing to remember, of course, with the history Graham, is that your bars are going to be connected, As you see here for part B for Part C were asked to do the relative frequency distribution. So now we're going to take each frequency and divided by the total number of data values, which the total number of data values is 42. So to find the relative frequency of a score of one, we do nine divided by 42 which is going to give us point 214 1st 4 of two, we do 11 divided by 42 which gives us 420.262 for a score of three. Reading 13. Divided by 42 which gives us 420.310 1st 44 We do six, divided by 42 which gives us 420.14 three and lastly, 1st 45 We do three divided by 42 which would give us 420.71 And you want to make sure that your relative frequencies add up to 1.0 or 100%. If you were viewing them as persons, there are a few ways that we can find the percentage of students who will receive college credit. Um, one way you can do this is by adding up the number of students that scored a 34 and five so 13 plus six plus three. And divide that by your total number of students 42. That would give us 22/42 which would give us 0.5 to 4. And we want this answer as a percent so you would multiply that I 100 and that would give you 52.4% of students who would receive college credit

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