How many data points are above the median?
How many data points are below the 1st quartile?
How many data points are between the 1st and the 3rd quartiles, or in the interquartile range (IQR)?
How many data points are above the median? How many data points are below the 1st quartile? How many data points are between the 1st and the 3rd quartiles, or in the interquartile range (IQR)
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To answer your questions, let’s define the terms involved:
1. Median: The median is the middle value of a data set when it is ordered. Half of the data points will be above the median and half below.
2. First Quartile (Q1): This is the median of the lower half of the data, which means that 25% of the data points are below this value.
3. Third Quartile (Q3): This is the median of the upper half of the data, meaning that 75% of the data points are below Q3.
4. Interquartile Range (IQR): This is the range between the first quartile (Q1) and the third quartile (Q3), representing the middle 50% of the data.
Now, here’s how to answer your specific questions:
1. Data points above the median: In a data set with n data points, if n is odd, there will be (n-1)/2 data points above the median, and if n is even, there will be n/2 data points above the median.
2. Data points below the 1st quartile: There will always be 25% of the data points below Q1.
3. Data points in the IQR: The number of data points between Q1 and Q3 is 50% of the total data set because the IQR contains the middle