Extending Concepts

M...

Question

Extending Concepts

Midquartile Another measure of position is called the midquartile. You can find the midquartile of a data set by using the formula below.

Midquartile = (Q₁ + Q₃) / 2

In Exercises 55 and 56, find the midquartile of the data set.

5 7 1 2 3 10 8 7 5 3

Accepted Answer

Hello. In this video, we are given a data set from 1215, 1018, 1420, 1317, 11, and 16, and we want to find the mid-quartile. So, in order to find the mid-quartile, the first thing we want to do is we want to organize our data set from least to greatest. By doing this, we get the following data set. We get 10, 1112, 1314, 1516, 1718, and 20. Now, the mid mid-quartile is defined as the following. It is going to be the first quartile of the data set, plus the 3rd quartile of the data set, and that we are going to average it, so we are going to divide the sum by 2. This is going to be the definition of our mid-quartile. So the first thing we need to do is we need to identify our first and our 3rd quartile. Now, we have a total data set of 10 values. So what we're going to do is we are going to group these values by grouping up the 1st 5 together. And grouping up the last 5 together. So, let's go ahead and make a split in between the data set. Now, the reason why we split this data set is because the quartiles we're looking for are the medians of the upper and lower halves of the data set. Now, for the first quartile, the 1st quartile is going to be the median of the first half of the data set. So it is going to be the median of the 1st 5 values, and that is going to be 12. So we have a first quartile of 12. Now, for the 3rd quartile, the 3rd quartile is the median of the upper half of the data set, and the median of the upper half of the data set is going to be 17. So, since we have the first and 3rd quartiles, in order to find the mid-quartile, we are going to take the sum of these two quartiles and average them. So our mid-quartile is going to be 12 + 17 divided by 2, and by simplifying, this is going to give us 24 divided by 2. Which is equal Oh, sorry, not 24, 29 divided by 2. And 29 divided by 2 is going to simplify to be 14.5. So, the solution to this problem is going to be a mid-quartile of 14.5, and the overall solution is going to be B. So I hope this video helps you understanding how to find the mid quartile of a data set, and we will go ahead and see you all in the next video.

��app

Extending Concepts

Midquartile Another measure of position is called the midquartile. You can find the midquartile of a data set by using the formula below.
Midquartile = (Q₁ + Q₃) / 2
In Exercises 55 and 56, find the midquartile of the data set.

5 7 1 2 3 10 8 7 5 3

Key Concepts

Midquartile

Quartiles

Data Set

Watch next

����app

Extending ConceptsMidquartile Another measure of position is called the midquartile. You can find the midquartile of a data set by using the formula below.Midquartile = (Q₁ + Q₃) / 2In Exercises 55 and 56, find the midquartile of the data set.5 7 1 2 3 10 8 7 5 3