Using and Interpreting Concepts

Question

Using and Interpreting Concepts Finding Quartiles, Interquartile Range, and Outliers In Exercises 11 and 12,

(c) identify any outliers.

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Accepted Answer

Hi, everyone, let's take a look at this practice problem. This problem says consider the following set of test scores 68, 72, 65, 70, 69, 74, 70, 71, 67, 73, 80, 72, 70, 75, and 77. Identify any outliers, if any. And we're going 4 possible choices as our answers. For choice A, we have yes, there is one outlier below the lower bound, which is 65. For choice B, then yes, there is one outlier above the upper bound, which is 80. For choice C, we have, yes, there are outliers on both ends, and we have 65 and 80, and for choice D we have no, there are no outliers. So, we're asked to identify any outliers in our data set, and in order to do that, we first need to find our 1st and 3rd quartile. Values, so we're looking for Q1 and Q3. So, in order to do that, we need to first order our data here in ascending order. So, doing so, starting with the lowest value, will have 65. Then 67. 68 69. 70 70 again. 70 for a third time. 71 72. 72 again. 73. 74. 75 77 And 80. The first thing we want to do is to find our median, which is also our second quartile. We'll label that as Q2. And recall that the median is the value that shows up in the middle of our data set, once we have ordered it in ascending order. So since we have 15 data points here, we're looking for the 8th data point in our sequence, and that actually corresponds to 71. So that means that Q2 is equal to 71. Now, the reason why we wanted to find the median is because we'll need to use that location in our data set to determine our values for the first quartile and third quartile Q1 and Q3. So looking for our first quartile, Q1, recall that that is going to be the median median of the data set that of the values that fall below our median. So we're looking at the median of the values between 65 and 70, since those are the values that flow fall below our median. So here we have 7 data points, and so, we're looking for the value in the middle, so that will be the 4th data point, which corresponds to a value of 69. So that means that Q1 is equal to 69. We'll do something similar for a 3rd quartile, Q3. And so here we're looking for the median of the upper half of our data set. So we're looking at for the median. Of the data between 72 and 80. And so again, here we have 7 points. And that means we're looking for the 4th value in our data set here, which corresponds to 74. So that means that Q3 is equal to 74. Now, we're ultimately interested in finding any outliers, and for that we're gonna need our interquartile range. So, recall for our interquartile range, which we'll label as IQR, but that is going to be equal to. Q 3 minus Q 1. That's going to be equal to 74 minus 69. Which when we do that subtraction is equal to 5. So we will now use this inner quartile range to find our upper and lower bounds or our outliers. So, looking at the lower bound, which we'll label as L. Recall that that is going to be equal to you won. -1.5, multiplied by our interquartile range IQR. So this is going to be equal to. 69. -1.5, multiplied by 5. Which we only evaluate this, this expression is going to be equal to. 61.5. We'll do something similar for upper bound, which we'll label as you and recall that our upper bound is going to be equal to U3. Plus 1.5, multiplied by interquartile range IQR. So this is going to be equal to. 74. Plus 1.5, multiplied by 5. Which one we evaluate this expression is going to be equal to? 81.5. And so now if we look at our values and see if we have any values that are below our lower bound or above our upper bound, we see that all of our values in our data set fall between our lower bound and upper bound. That means that we have no outliers. So that is going to be the answer that we're looking for, for this problem. And if we compare what we have found to our answer choices, we see that the correct answer choice corresponds to answer choice D. So, I hope that this explanation has been useful, and I'll see you in the next video.

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Using and Interpreting Concepts

Using and Interpreting Concepts Finding Quartiles, Interquartile Range, and Outliers In Exercises 11 and 12,
(c) identify any outliers.

56 63 51 60 57 60 60 54 63 59 80 63 60 62 65

Key Concepts

Quartiles

Interquartile Range (IQR)

Outliers

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Using and Interpreting ConceptsUsing and Interpreting Concepts Finding Quartiles, Interquartile Range, and Outliers In Exercises 11 and 12,(c) identify any outliers.56 63 51 60 57 60 60 54 63 59 80 63 60 62 65