Previously we listed the data in order, smallest to largest, and found the median of 49. To find the lower quartile, find the median of the lower half of the data. The lower half consists of all values that sit below the median but not including the median. The lower half and you can verify that n is odd for the lower half which means the median will be the single middle number. 17 26 30 41 43 46 48 Find the lower quartile. X 20 To find the upper quartile, find the median of the upper half of the data. The upper half consists of all values that sit above the median but not including the median. The upper hat and you can verify that n is odd for the upper half which means the median will be the single middle number. 53 53 54 63 69 72 78 Find the upper quartile. 69 X The interquartile range is a measure of variability that is resistant to outliers and is found as follows. interquartile range = upper quartile lower quartile Find the interquartile range.
Previously we listed the data in order, smallest to largest, and found the median of 49. To find the lower quartile, find the median of the lower half of the data. The lower half consists of all values that sit below the median but not including the median. The lower half and you can verify that n is odd for the lower half which means the median will be the single middle number. 17 26 30 41 43 46 48 Find the lower quartile. X 20 To find the upper quartile, find the median of the upper half of the data. The upper half consists of all values that sit above the median but not including the median. The upper hat and you can verify that n is odd for the upper half which means the median will be the single middle number. 53 53 54 63 69 72 78 Find the upper quartile. 69 X The interquartile range is a measure of variability that is resistant to outliers and is found as follows. interquartile range = upper quartile lower quartile Find the interquartile range.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Understanding Lower and Upper Quartiles
The next step is to find the lower and upper quartiles. The lower quartile is the median of the lower half while the upper quartile is the median of the upper half. Recall that 25% of the data are less than the lower quartile while 75% of the data are greater. Similarly, 75% of the data are less than the upper quartile while 25% of the data are greater.
Previously we listed the data in order, smallest to largest, and found the median of 49.
#### Finding the Lower Quartile
To find the lower quartile, find the median of the lower half of the data. The lower half consists of all values that sit below the median but not including the median. The lower half is listed below, and you can verify that *n* is odd for the lower half which means the median will be the single middle number.
\[ 17, \ 26, \ 30, \ 41, \ 43, \ 46, \ 48 \]
**Find the lower quartile.**
\[ 20 \times \]
#### Finding the Upper Quartile
To find the upper quartile, find the median of the upper half of the data. The upper half consists of all values that sit above the median but not including the median. The upper half is listed below, and you can verify that *n* is odd for the upper half which means the median will be the single middle number.
\[ 53, \ 53, \ 54, \ 63, \ 69, \ 72, \ 78 \]
**Find the upper quartile.**
\[ 69 \times \]
#### Finding the Interquartile Range
The interquartile range is a measure of variability that is resistant to outliers and is found as follows:
\[ \text{Interquartile Range} = \text{Upper Quartile} - \text{Lower Quartile} \]
**Find the interquartile range.**
\[ 49 \times \]
### Summary
The lower quartile and upper quartile are essential to understanding the distribution of data. They help identify the spread and concentration of data points, positioning 25% and 75% thresholds, which are crucial for statistical analysis. The interquartile range provides a measure that is resistant to the effects of outliers, offering a clearer picture of variability in the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc4971f23-5570-4fed-8cd6-5e1a07d18a42%2Fa4dc78f9-17a8-4a3c-85f4-36098673a79c%2Fhxdpj5b_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding Lower and Upper Quartiles
The next step is to find the lower and upper quartiles. The lower quartile is the median of the lower half while the upper quartile is the median of the upper half. Recall that 25% of the data are less than the lower quartile while 75% of the data are greater. Similarly, 75% of the data are less than the upper quartile while 25% of the data are greater.
Previously we listed the data in order, smallest to largest, and found the median of 49.
#### Finding the Lower Quartile
To find the lower quartile, find the median of the lower half of the data. The lower half consists of all values that sit below the median but not including the median. The lower half is listed below, and you can verify that *n* is odd for the lower half which means the median will be the single middle number.
\[ 17, \ 26, \ 30, \ 41, \ 43, \ 46, \ 48 \]
**Find the lower quartile.**
\[ 20 \times \]
#### Finding the Upper Quartile
To find the upper quartile, find the median of the upper half of the data. The upper half consists of all values that sit above the median but not including the median. The upper half is listed below, and you can verify that *n* is odd for the upper half which means the median will be the single middle number.
\[ 53, \ 53, \ 54, \ 63, \ 69, \ 72, \ 78 \]
**Find the upper quartile.**
\[ 69 \times \]
#### Finding the Interquartile Range
The interquartile range is a measure of variability that is resistant to outliers and is found as follows:
\[ \text{Interquartile Range} = \text{Upper Quartile} - \text{Lower Quartile} \]
**Find the interquartile range.**
\[ 49 \times \]
### Summary
The lower quartile and upper quartile are essential to understanding the distribution of data. They help identify the spread and concentration of data points, positioning 25% and 75% thresholds, which are crucial for statistical analysis. The interquartile range provides a measure that is resistant to the effects of outliers, offering a clearer picture of variability in the
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