Using and Interpreting Concepts

Question

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

(a) find the quartiles

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 68, 72, 65, 70, 69, 74, 70, 71, 67, 73, 80, 72, 70, 75, and 77. Find the first quartile Q1, the median Q2, and the third quartile Q3. So we're asked to find the first quartile, the median and 3rd quartile for this data set. So, the first thing we need to do is to order our data set in ascending order. So, starting with the smallest value, we'll have 65. Then 67. 68 69 70 70 again. And 70 for a third time. 71 72. 72 again. 73 74. 75 77 And 80 So the first value that we're going to find is going to be our median, which is Q2. And recall that the median is the value that is in the middle of our data set once we have put it in ascending order. So here we have 15 data points, so we're looking for the 8th data point in our data set here. And so when we look at the 8th data point, we see that it has a value of 71. So that means that Q2 is going to be equal to 71. Next, we'll find our first quartile, Q1. And so this is going to be the median of the set of data that is below our median. So, we're going to be looking at the median for the data set between 65 and 70. So here we have 7 data points, and so we're looking for the data point that is in the middle, so we'll look at the 4th data point, which turns out to be 69. So that means that Q1 is going to be equal to 69. We'll do something similar for our 3rd quartile, Q3. Here, we're gonna be looking at the median of the upper half of our data set. So, the data set that is above our median, so we'll look at the values between 72 and 80. So again, here we have 7 data points, and so we're going to choose the one in the middle, so that that will be the 4th data point, which turns out to be 74. So that means that Q3 is equal to 74. That means the answer for this problem is going to be that Q1 is equal to 69, Q2 is equal to 71, and Q3 is equal to 74. So that is the answer that we're looking for for this problem. 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,
(a) find the quartiles

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,(a) find the quartiles56 63 51 60 57 60 60 54 63 59 80 63 60 62 65