Using and Interpreting Concepts

Question

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

(b) find the interquartile range

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

Accepted Answer

Hi everyone. Let's take a look at this practice problem. This problem says consider the following set of test scores. Find the interquartile range. We're given the values of 68, 72, 65, 70, 69, 74, 70, 71, 67, 73, 80, 72, 70, 75, and 77. We're also given 4 possible choices as our answers. For choice A, we have 2, for choice B, we have 3, for choice C, we have 5, and for choice D, we have 6. So this problem we're asked to find our interquartile range, and in order to find our interquartile range, we'll need to find our first and 3rd quartile values. So to do that, we'll first need to rewrite our data in ascending order. So starting with the smallest value, we'll have 65. 67 68 69 70 70 again. 70 for a third time. 71 72. 72 again. 73. 74. 75 77 And 80. So the first thing we need to do is to find our median, which we'll label as Q2, since it's also our second quartile. Recall that the median is the value that is in the middle of our sequence once we have placed our data in ascending order. So since we have 15 data points here, we're going to be looking at the 8th number in our sequence here, and that actually corresponds to a value of 71. So that means that our median Q2 is going to be equal to 71. And so now we're going to use this median median value to determine our 1st and 3rd quartile. So, looking at the first quartile, Q1. We call that, that is the median of the data set that is below our median. So that is going to be the median of the data set between 65 and 70. And here we have 7 data points, and so we're looking for the value in the middle, so that will be the 4th value, which turns out to have a value of 69. So that means that Q1 is going to be equal to 69. Next, we'll need to find the value of 3rd quartile Q3. And recall that that is going to be the median of the upper half of our data set, so the data set that is above our median. So that's gonna be the data that between 72 and 80. So again, here we have 7 values, and so we're looking for the value in the middle. And that will be the 4th data point, which in this case, corresponds to a value of 74. So that means that Q3 is going to be equal to 74. And so now we have enough information to calculate our interquartile range, which we'll label as IUR. And we call that our interquartile range is going to be equal to Q3 minus Q1. Which is equal to, using the values that we just calculated, we'll have 74 minus 69. Which is going to be equal to 5. So our answer quartile range is equal to 5. So that is the answer that we're looking for for this problem. And if we look at our answer choices, this actually corresponds to answer choice C. So I hope that this explanation has been useful, and I'll see you in the next video.

Using and Interpreting Concepts

Using and Interpreting Concepts Finding Quartiles, Interquartile Range, and Outliers In Exercises 11 and 12,
(b) find the interquartile range

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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