In Exercises 7 and 8, use the data set shown in the table at t...

Question

In Exercises 7 and 8, use the data set shown in the table at the left, which represents the pollution indices (a unitless measure of pollution ranging from 0 to 100) for 24 U.S. cities. (Adapted from Numbeo)

Use a dot plot to display the data set. Describe any patterns.

Use a dot plot to display the data set. Describe any patterns.

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. The following are the noise levels recorded in units of decibels measured from 20 different classrooms. 48 55 55 52 49 53 51 61 54 50 57 53 55 52 53 49 645458 65 Construct a dot plot for this data set. What pattern do you observe from the distribution? Awesome. So it appears for this particular prompt we're asked to create a dotbot for this particular data set, and we're also asked to determine what pattern we observe from our dotbot that we create together. So we're ultimately trying to solve for two separate answers. So with that in mind, now that we know what we're ultimately trying to solve for, our first step in order to help us create our dot plot, because then later after we create our dot plot, we have to observe the pattern that we see on our dot plot from the distribution. So our first step to create our dot plot is we need to list our data. In increasing order, so we need to write our data from the smallest number to the largest number in numerical order. So when we do that, or the fancy way of saying is when we Arrange our data set in ascending order. We will achieve the following. You'll get 48 49 49 50 51 52 52 53 53 53 54 54, 55 55 55 57 58 61 64, and 65. Awesome. Our second step now. we need to draw our horizontal axis, so we need to label the axis with the possible noise levels. So to minimize the values to be written along the horizontal, we may write the values in increments of two, such as 48, 50, 52. Our 3rd step is we need to place the dots for each value. So for each occurrence of a noise level in that data set, we need to place a dot above that value on the axis. Awesome. And if the value occurs more than once, we need to stack the dots vertically. So since 48 occurs once we only place one dot above our value on our dot plot above our vertical axis for our dot plot, and 49 occurs twice, we have to put one dot and then a dot on top of it. And then 53 occurs 3 times, so we need to stack 3 dots above the value of 53. Fantastic. So with that in mind, I've gone ahead and made a computer generalized. graph for our problem for our dot plot, and like we discussed, as we could see, We have our dot plot. And our dot plot Has all the values listed from our, once again, our 20 different classrooms, and if there's more than one value, you just stack it above vertically. Like for example, 53 is listed 3 times, so if we go between 52 and 54, we'll see it's listed 3 times. And it's also important when you're doing. And the dot plot is that you give it a title to label it, so we know that these are the classroom noise levels and units of decibels. It's important to list what units it's in. So now, as for our second answer, we need to note that from our dot plot, as you can see looking at how our data is laid out, we can observe that the noise levels are mostly clustered between the 49 decibel range to the 55 decibel range. Inclusive, with a few higher values at 61, 64, and 65 decibels that appear to be outliers. So, our outlier values once again are 61, 64, and 65 that appear to be outliers. So that means that we could safely say, For our 2nd. Final answer that we're ultimately trying to solve for, we could put a box around our answers that the noise levels are are mostly clustered between 49 decibels and 55 decibels with a few higher values, 61, 64, and 65 decibels that appear to be outliers. Awesome, and that's it. We've officially solved for this problem. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

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