Q_1, Median, and Q_3 of A,B,C,D & E

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In summary, the data set consists of five numbers: 18, 19, 23, 31, and 36. The first quartile (Q1) is 19, the median is 23, and the third quartile (Q3) is 31. The interquartile range is 11, which is calculated by subtracting Q1 from Q3. However, W|A gives a slightly different result due to interpolation between the numbers.
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karush
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View attachment 1129
\(\displaystyle A=18\) (first data in list)
\(\displaystyle B=19 Q_1\)
\(\displaystyle C=23\) (median of list)
\(\displaystyle D=31 Q_3\)
\(\displaystyle E=36\) (last data of list)

altho the problem doesn't ask for it, but W|A says the interquartile range is \(\displaystyle 11\) but here
\(\displaystyle Q_3-Q_1\) is \(\displaystyle 31-19=12\)?
 
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Re: box plot

karush said:
View attachment 1129
\(\displaystyle A=18\) (first data in list)
\(\displaystyle B=19 Q_1\)
\(\displaystyle C=23\) (median of list)
\(\displaystyle D=31 Q_3\)
\(\displaystyle E=36\) (last data of list)

altho the problem doesn't ask for it, but W|A says the interquartile range is \(\displaystyle 11\) but here
\(\displaystyle Q_3-Q_1\) is \(\displaystyle 31-19=12\)?

Hi karush!

Your answers are all correct using the regular and simple method to determine the quartiles.
The reason W|A gives something different is because W|A interpolates between the numbers.
The actual first quartile is between 19 and 20. W|A interpolates and makes it \(\displaystyle 19\frac 14\).
Similarly W|A interpolates the third quartile to be \(\displaystyle 30\frac 14\), resulting in an interquartile range of \(\displaystyle 11\).
 

FAQ: Q_1, Median, and Q_3 of A,B,C,D & E

What are Q1, Median, and Q3?

Q1, Median, and Q3 are measures of central tendency used in statistics. They are also known as the first quartile, median, and third quartile, respectively. These values divide a dataset into four equal parts, with Q1 representing the 25th percentile, the median representing the 50th percentile, and Q3 representing the 75th percentile.

How are Q1, Median, and Q3 calculated?

To calculate Q1, the dataset is first sorted in ascending order. Then, the value at the 25th percentile is identified. If the number of data points is odd, the median is used as Q1. If the number of data points is even, the median is calculated by taking the average of the two middle values. The same process is followed to calculate Q3, but using the 75th percentile instead.

What information do Q1, Median, and Q3 provide?

Q1, Median, and Q3 provide information about the spread of the data. They can help identify the range of values that most of the data falls within, as well as any potential outliers. They can also be used to compare different datasets and determine if they have similar distributions.

How do Q1, Median, and Q3 relate to the mean?

Q1, Median, and Q3 are measures of central tendency, just like the mean. However, unlike the mean, they are not affected by extreme values or outliers in the dataset. This makes them more robust measures of central tendency in skewed distributions.

Why are Q1, Median, and Q3 important in data analysis?

Q1, Median, and Q3 provide valuable information about the distribution of a dataset. They can help identify any potential outliers or unusual patterns in the data. They are also used in various statistical analyses, such as box plots and quartile deviation, to better understand and interpret the data.

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