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4. (14 pts total) Ozone levels around Los Angeles have been measured as high as 220 parts per billion (ppb). Concentrations this high can cause they eyes to burn and are a hazard to both plant and animal life. These data were obtained on the ozone level in a forested area near Seattle, Washington (based on information found in "Twigs", American Forests, April 1990, p. 71): 160 160 161 161 162 162 162 163 163 163 164 165 167 167 168 169 170 172 173 176 178 179 180 185 196 (a) (10 pts) Find the "5 number summary" (min, first quartile, median, third quartile, and maximum) and make an accurate "basic" boxplot for these data (include an accurate scale next to or underneath your boxplot). Do the data seem skewed left, skewed right, or symmetric? (b) (4 pts) Use these data to give unbiased estimates the sample mean and sample variance of the ozone level in this area. You may use your calculator without showing work, but write down the appropriate symbols for these quantities (and, if you want to show work just in case your numbers are wrong, write down formulas that can be used to find these quantities).

          4. (14 pts total) Ozone levels around Los Angeles have been measured as high as 220 parts per billion (ppb). Concentrations this high can cause they eyes to burn and are a hazard to both plant and animal life. These data were obtained on the ozone level in a forested area near Seattle, Washington (based on information found in "Twigs", American Forests, April 1990, p. 71):
160 160 161 161 162 162 162 163 163
163 164 165 167 167 168 169 170 172
173 176 178 179 180 185 196
(a) (10 pts) Find the "5 number summary" (min, first quartile, median, third quartile, and maximum) and make an accurate "basic" boxplot for these data (include an accurate scale next to or underneath your boxplot). Do the data seem skewed left, skewed right, or symmetric?
(b) (4 pts) Use these data to give unbiased estimates the sample mean and sample variance of the ozone level in this area. You may use your calculator without showing work, but write down the appropriate symbols for these quantities (and, if you want to show work just in case your numbers are wrong, write down formulas that can be used to find these quantities).

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4. (14 pts total) Ozone levels around Los Angeles have been measured as high as 220 parts per billion (ppb). Concentrations this high can cause they eyes to burn and are a hazard to both plant and animal life. These data were obtained on the ozone level in a forested area near Seattle, Washington (based on information found in "Twigs", American Forests, April 1990, p. 71):
160 160 161 161 162 162 162 163 163
163 164 165 167 167 168 169 170 172
173 176 178 179 180 185 196
(a) (10 pts) Find the "5 number summary" (min, first quartile, median, third quartile, and maximum) and make an accurate "basic" boxplot for these data (include an accurate scale next to or underneath your boxplot). Do the data seem skewed left, skewed right, or symmetric?
(b) (4 pts) Use these data to give unbiased estimates the sample mean and sample variance of the ozone level in this area. You may use your calculator without showing work, but write down the appropriate symbols for these quantities (and, if you want to show work just in case your numbers are wrong, write down formulas that can be used to find these quantities).

Added by Kristin T.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Lucas Finney

03/10/2023

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To do this, we'll find the minimum, first quartile, median, third quartile, and maximum of the given data. Show more…

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4. (14 pts total) Ozone levels around Los Angeles have been measured as high as 220 parts per billion (ppb). Concentrations this high can cause they eyes to burn and are a hazard to both plant and animal life. These data were obtained on the ozone level in a forested area near Seattle, Washington (based on information found in "Twigs", American Forests, April 1990, p. 71): 160 160 161 161 162 162 162 163 163 163 164 165 167 167 168 169 170 172 173 176 178 179 180 185 196 (a) (10 pts) Find the "5 number summary" (min, first quartile, median, third quartile, and maximum) and make an accurate "basic" boxplot for these data (include an accurate scale next to or underneath your boxplot). Do the data seem skewed left, skewed right, or symmetric? (b) (4 pts) Use these data to give unbiased estimates the sample mean and sample variance of the ozone level in this area. You may use your calculator without showing work, but write down the appropriate symbols for these quantities (and, if you want to show work just in case your numbers are wrong, write down formulas that can be used to find these quantities).

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00:01 So for this problem, the first thing that'll note is that, well, we are asked to find the five number summary.

00:06 So we have min, q1, median, q3, and maximum.

00:15 So we can note that with the numbers given, they're actually already arranged in ascending order, so it's not too difficult to find these.

00:24 Specifically, the minimum and the maximum are very easy.

00:27 We can see that the minimum value is 160 and the maximum value is 196.

00:31 Then to find the median, what i'll do is first find the rank of the median by determining the number of data points that we have.

00:42 So i'll note that we have 25 observations, the rank will be 25 plus 1 divided by 2.

00:50 So it would be 26 over 2, which is 13.

00:53 So we have that the median is going to be the 13th measurement in order.

00:58 So i'm going to pause and determine what value that is.

01:01 So we have that the 13th value is going to be 167.

01:07 To find the rank of the first quartile, we take one quarter of 26.

01:15 So let's see here, 26 over 4 gives a result of 6 .5.

01:19 So that means that the first quartile is going to be the average of the 6th and 7th values.

01:25 But we'll find that both x6 and x7 are equal to each other.

01:30 They're both equal to 162.

01:32 So the first quartile is just 162.

01:36 And then for the third quartile, the rank of q3, that's going to be three quarters of 26, or three times 26 over four, which gives a result of 19 .5, suggesting that our third quartile will be the average of the 19th and 20th values.

01:55 So, i'll note that x -19 is equal to 173, x -20 is equal to 117, 76.

02:08 So the midpoint between those two values would be at 174 .5.

02:14 So that gives us our third quartile, 174 .5.

02:19 Now i'm going to pause for a second and swap my background here...

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